Способ 3. Если воспользоваться геометрическим смыслом квадратного трехчлена, то, обращаясь к равносильной уравнению (1) в системе (2), приходим к выводу, что уравнение (1)будет иметь корни
![](data:image/gif;base64,R0lGODlhEAAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAAMAAwAhAAAAAAAAAAAHR0AAAAAMwAdSR0dSAAyWgAzWwAzWh1GbB1IbjQ0HTNZf0gcAEgdAEceM1szAERqe11/f1VmZkRubl13d2xGHW5IHX9ZM25GM39uSHd3ZmaIiIBdM4iIZgUmICCO5OgFwhiU4wEgrLgNSjw6tqgByUjkrJXoEVgAIMBjEplMCkMAOw==)
и
![](data:image/gif;base64,R0lGODlhEQAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAANAAwAhQAAAAAAAAAAHR0AAAAdRx0dSAAAqgAyWAAzWh1GbB1IbjMAADIAMjQ0HT8/SDNZfzNdgEgcAEcdAFozHVtISERqe1VmZl1/f0huf25IHWxGHX9ZM25GM31ZMX9uSHd3XX9/XXd3ZmaIiIBdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwYxQIBwSCSOAoJhoEg8ABDMoWeQiBIj1iHnOVwEqlaHkCFcCiUBxXCSbTMhbmc7QAcEAQA7)
в том случае, когда корни квадратного трехчлена
![](data:image/gif;base64,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)
не меньше
![](data:image/gif;base64,R0lGODlhEAApAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAJACMAhQAAAAAAAAAAHQEAAAAAMwAcSAAcRh0dSQAAqgAzWgAzWx1GajMAADFZfTNZfzNdgEYcAEgcAEgeNFgyAFozAFszHUhZf1VmZl1/f0hzgGxGHW5IHWpIHX1ZMWZmVX9/XXd3XXtqRHd3ZmaIiIBdSIiIZqoAAP8AAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZGQIBwSBRCCkUAI5AcIpOapvBZjEqpRGsTO5w0lwGBdEwum5uBtFp9bruT4KJkOBgnmpTxo3loVppaRB1DIURrBEIcawF3QQA7)
. Аналитически соответствующие условия записываются в виде системы
![](data:image/gif;base64,R0lGODlhpACIAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgChAIMAhgAAAAAAAAAAHR4AHh0AHR0AAAAeHgAAMx0AMx0AMgAcSB0dSAAdSB0dSQAdSQAzWgAzWx0zWwAyWgAzWQszbR1JSR1Ibh1GbB1MfxVAgDMAADMLFDIAHSgGFTMAHTMLCzMAMzIAMjQeSDMeRzMzWzNbWzNZfzNGbjNdgDNbgDduf0gcAEgdAEkdAEkdHUceM0geNFszAFozHVozAFoyAFoyHVszHV0oBl4oC1szM1oyMklJHUZGM0hZf1lZf0hZfVl/WUhuf11/f0B/f1V3d0Rqe113d1VmZmxGHW5IHX9ZM25GM39ZSHd3XWZmVXd3VX9/XX9uSHtqRGZ3d3d3ZmaIiIBAFYBbM4BdM4BdSIBuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwf/gACCg4SFhoeIiYqLjI2Oj5CRjjECkpaXmJmam4sanJ+goaKbSKOmp6ipAEGqra6vjTmws7S1tre4oLK5vL2+v8Ciu8HExcbHvsPIy8zNzprKz9LT1NI61djZ2sAv297f4Krd4eTl5pLj5+rr7ADp7fDx2u+DMQH39w+YK4kBB4ga7nECoUkgMyT/BGlQYCkgw0IaEg5SkpCgIImZBmBKqMGEL3qDZkAgFOASkoeDNIwsZLEQB0QgFyGwxG8QSmOeCOW0dBMAxkEWDkUApY8QlkVRCLASRODjIYqFVhSNdFIngIASXxpakCgmSQE8GAxKcCjAykMYNaRAJtaqIXxw/w+hvBKgwaB/V34CuKe30UoNF1L2O5TXLa8Oh2oSKhBUUtW7JC8eShIgsCB7cO+dBSBykOKrlhEV+ImxwDEpSgv1dTQ3LQCEiD43kigF4qICBnoMSroUQNNeMdsOKmkIc+bNr20P+r16xlpDMWcQkqrzuaECwgmxIJQ92E5BxDH1lHi2yCG7kCQoLOljbNlFbTWgcEoyc/dIAQNUqn82Rv0A9w0CAyJ8XSVRKYYgR2B48jjiQYOaeGWLRqZ8B6ErLV0IiYQaduhhLRx+KOKIp4RI4okoZmJiiiy2yMiKLsYooyAwJsICg5zMkI8mK/SEogyiCDeVJA6ZU2MiIYTyWf+AjzzW4pCcoNSYeEZqIl2RnBSgngib+EhiRABEUYB1mSjhT5RVZnKWhZqAmYmTKEonCGq9ZRKal5DgOU8mSQrS2Sbf9WmSntqogMlUq/E0CJOPEIrNBwWZFcqNAGaS337hfGDojMVAyumnjRw14lDUSNoho6dkZpAlOMYD5WWqmlrMaBAquEisuOITSa6K4KbbcLiGE1orxsFlayPYgfpLqxBG08yxykY7CpDS/lKnI/l5NIqOzEKSnzmeQjIgeNqCMkNbMbzqyLh7kdibbJ+EhmoiWRSibjZHHgLtJSw8hKCV+14oGxL6ATBvr6KQ6U2+haAniGJs7ppoJA6f2Jv/nIMovKGBm9iQ5iYYkXUJxjE4usi/J4am21TweluuoJIoMUht4TC8Fz7/xKDeVQGUgEm/i15iJs4jZgbsP27yu6oklBlLjs3VRq0O1FJXXbPVuCCGtS1Ub+01NV1L1snXn/g3CdnujNLjZGiLElAiHnsNNYd6ctU2JCckgvIh5mFt8xKLmHw3KYuMsLXNJAQ+uCZRnLwItVbbPKxci2dyxSI0OO53IwFNDtA9mHKy9iWCR1V6KEtf8qCoAFihyQ34BXA6RLPzXLsiScymULnQLYIxIRlkckPwkdwuyA6KeAUnJ7Ia8pnxAEBViOvCKyrJfHpKCP2tiKTGVFc2FsjL//KNJE4+I+efXDCqtBLimiW/D3L5m4UUiw9ytQ+TfSK1Q9xJAFMqjGBgooiI3cJHsTrE8uynGULAiYGy+hMAVqAxQbRPNYupICNEVoj5FSJXrdoba3aVmfn0DhGnk54gOBiZRHjPN+BDBBIOxgkIbiZ96LsdDg0xA5bpaxHbEcQMLzElQnjQJNZL4gkpd7b1+EwS8dFg2rqXCCk6woqGuJQlcpcIdukEdI8oUNKAZbS3MKgFNEwOIqiHCdhhLVxCVM9MEkE8TNRRapr64MTYeIhsJcKNVoPjI+44mW4BYHhb29Qj+JiIlgkCkFUTpCMowAgJDu5ajGgcIxwJAMhVzUaTj0gcJsJWucJtDZSlFAUmG5E3RKjsEKuUFiojJb5CiDKViWDdf1IniFlGLW5bxKUiPPcIszVCZsKcxMQUEjCphS6ZkggEADs=)
Решая эту систему, находим, что
![](data:image/gif;base64,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)
.
При
![](data:image/gif;base64,R0lGODlhLQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAoAAwAhQAAAAAAAAAAHQAAMx0AMgAdSB0dSB0dSR0zWwAzWwAzWgAyWh1GbDMAADIAHTMAMzNbWzNZfzNbgEgcAFszAFozAEZGM1lZf1l/WV1/f0huf1VmZl13d25IHWxGHX9ZM3d3XX9/XXtqRGZmVXd3VXd3ZmaIiIBdM4BuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZbQIBwSCwaj8ikcplsBALM6PIxHEivSw12W0QQPQEBoMBdGoiThLBRpDzfT7X0aQVUipKtGx4fdgIMAHVCBGVME0IKQ4hGfE9lEhRDToZMB0J0AA2DlUInb2QAQQA7)
уравнение (1) имеет решение
![](data:image/gif;base64,R0lGODlhIwATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAeAAwAhQAAAAAAAAAAHR0AAAAcSAAdSB0dSAAyWgAzWwAzWh1GbB1IbjMAADQ0HTNZf0gcAEgdAFszAFoyAERqe1VmZkhuf2xGHW5IHX9ZM25GM2ZmVX9/XX9uSHd3ZmaIiIBdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZLQIBwSCwaj8ikUkhYOomMQPNJBUyrS8v1ExAMA9jhdXgAIIqRgHodOBfHAM5AESbCAY/6UFvMABJHbGtHd3pDEldgQhABC2FRXQBBADs=)
.
Если же
![](data:image/gif;base64,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)
, т.е.
![](data:image/gif;base64,R0lGODlhLwATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAqAAwAhQAAAAAAAAAAHR0AAAAeHgAAMx0AMgAdSB0dSQAzWgAzWwAyWh1GbDMAADNbWzNZfzNbgDNdgEgcAEgeNFozAFszAFszHUZGM0hZf1lZf1l/WV1/f0huf1VmZm5IHWxGHX9ZM39ZSHd3XX9/XXtqRH9uSGZmVXd3VXd3ZmaIiIBdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZhQIBwSCwaj8ikcslsBAIPppQ5GUKn2CNnKMkqssnv8BMQAA7HANjY5YobygB6DUAMKUXIclAgVp6AT2JDW0J9QwZMAwR0Qwlce3QMQxgVQ05JcnSBh099DYdEKo0AgWoAQQA7)
, то уравнение (1) будет иметь один корень
![](data:image/gif;base64,R0lGODlhEQAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAANAAwAhQAAAAAAAAAAHR0AAAAdRx0dSAAAqgAyWAAzWh1GbB1Ibh1IajMAADMAMzQ0HT8/SDNZfzNdgEgcAEcdAFozHVtISERqe1VmZl1/f0huf25IHWxGHWpIHX9ZM25GM31ZMX9uSHd3XX9/XXd3ZmaIiIBdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwYxQIBwSCSWAoJhoEg8ABDMIWiQiBIl1qHnOWQEqtaHsCFcCieBxZCSbTMjbmc7QAcEAQA7)
. При
![](data:image/gif;base64,R0lGODlhLQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAoAAwAhQAAAAAAAAAAHR0AAAAAMx0AMgAdSB0dSB0dSR0zWwAzWwAzWgAyWh1Ibh1GbDMAADIAHTMAMzNbWzNZfzNbgEgcAFszAFozAFoyAEZGM1lZf1l/WV1/f0huf1VmZl13d25IHWxGHX9ZM3d3XX9/XXtqRH9uSGZmVXd3VXd3ZmaIiIBdM4BuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZmQIBwSCwaj8ikcpl8BALM6DIyJEivyw6W2NgmiKGAAGBIhrvYA7GiED6QFugW8LQCLkVKERPQw5+AT21CIAEOAHZCBUYDcnNDFUILkElxh48AFBZDTkyOWAhCdQAPiUkgUSuAZQBBADs=)
решений нет.
Способ 4. Рассмотрим графики функций
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,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)
заданных соответственно левой и правой частями уравнения (6.1).
Абсциссы точек пересечения этих графиков и будут решениями уравнения (1). При
![](data:image/gif;base64,R0lGODlhLQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAoAAwAhQAAAAAAAAAAHR0AAAAAMx0AMgAdSB0dSB0dSR0zWwAzWwAzWgAyWh1Ibh1GbDMAADIAHTMAMzNbWzNZfzNbgEgcAFszAFozAFoyAEZGM1lZf1l/WV1/f0huf1VmZl13d25IHWxGHX9ZM3d3XX9/XXtqRH9uSGZmVXd3VXd3ZmaIiIBdM4BuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZmQIBwSCwaj8ikcpl8BALM6DIyJEivyw6W2NgmiKGAAGBIhrvYA7GiED6QFugW8LQCLkVKERPQw5+AT21CIAEOAHZCBUYDcnNDFUILkElxh48AFBZDTkyOWAhCdQAPiUkgUSuAZQBBADs=)
графики не пересекаются (см. рис. 6.1) и значит уравнение (1) решений не имеет.
При
![](data:image/gif;base64,R0lGODlhLQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAoAAwAhQAAAAAAAAAAHQAAMx0AMgAdSB0dSB0dSR0zWwAzWwAzWgAyWh1GbDMAADIAHTMAMzNbWzNZfzNbgEgcAFszAFozAEZGM1lZf1l/WV1/f0huf1VmZl13d25IHWxGHX9ZM3d3XX9/XXtqRGZmVXd3VXd3ZmaIiIBdM4BuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZbQIBwSCwaj8ikcplsBALM6PIxHEivSw12W0QQPQEBoMBdGoiThLBRpDzfT7X0aQVUipKtGx4fdgIMAHVCBGVME0IKQ4hGfE9lEhRDToZMB0J0AA2DlUInb2QAQQA7)
графики касаются и уравнение (1) имеет один корень
![](data:image/gif;base64,R0lGODlhIwATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAeAAwAhQAAAAAAAAEAAAEAHR0AAAAAHgAcSAAdRx0dRwAcRgAAqgAyWAAzWh1Ibh1IajIAADQ0HTNZf0YcAEgcAFUAAEcdAFozAFgyAERqe1VmZkhzgGxGHW5IHWpIHX9ZM25GM39ZNWZmVX9/XX9uSHd3ZmaIiIBdM4iIZqoAAP8AAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZLQIBwSCwaj8ikUmhYOokPQfNJBUyry83VFBgMA9jhdbgAMIqWgHodOBfHgBGhESbCAZP6UFv8mI9sa0d3ekMXCV9DFQEOYQ9qBQBBADs=)
.
При
![](data:image/gif;base64,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)
уравнение (1) будет иметь корни
![](data:image/gif;base64,R0lGODlhEAAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAAMAAwAhAAAAAAAAAAAHR0AAAAAMwAdSB0dSAAyWgAzWwAzWh1GbB1IbjQ0HTNZf0gcAEgdAEceM1szAERqe11/f1VmZkRubl13d25IHWxGHX9ZM25GM39uSHd3ZmaIiIBdM4iIZgUmICCO5OgFwhiU4wEgrLgNSjw6tqgByUjkrJXoEVgAIMBjEplMCkMAOw==)
и
![](data:image/gif;base64,R0lGODlhEQAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAANAAwAhQAAAAAAAAAAHR0AAAAdRx0dSAAAqgAyWAAzWh1GbB1IbjMAADIAMjQ0HT8/SDNZfzNdgEgcAEcdAFozHVtISERqe1VmZl1/f0huf25IHWxGHX9ZM25GM31ZMX9uSHd3XX9/XXd3ZmaIiIBdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwYxQIBwSCSOAoJhoEg8ABDMoWeQiBIj1iHnOVwEqlaHkCFcCiUBxXCSbTMhbmc7QAcEAQA7)
, определяемые формулами (3) (см. рис. 6.2).
![](data:image/jpeg;base64,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)
При
![](data:image/gif;base64,R0lGODlhLQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwApAAwAhQAAAAAAAAAAHR0AAAAAMx0AMgAdSB0dSQAzWgAzWwAyWh1Ibh1GbDMAADNbWzNZfzNbgDNdgEgcAEgeNFozAFszAFoyAFszHUZGM0hZf1lZf1l/WV1/f0huf25IHWxGHX9ZM39ZSHd3XX9/XXtqRH9uSGZmVXd3VXd3ZmaIiIBdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZoQIBwSCwaj8ikcqlsBALMKHMyhEqvSwS2uNhSip+AAGBIhrtbAGQoSQgbyIo1DTgMv8Q10RLQH+VPgQFuQhdEBEQFRgNzaR9FWkISSXIMWyBDJAAVQ05MjZ+BiABPiA2jSh5RHoKDAEEAOw==)
графики функций
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,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)
пересекаются в одной точке, и значит уравнение (1) имеет одно решение
![](data:image/gif;base64,R0lGODlhEQAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAANAAwAhQAAAAAAAAAAHR0AAAAdRx0dSAAAqgAyWAAzWh1GbB1IbjMAADIAMjQ0HT8/SDNZfzNdgEgcAEcdAFozHVtISERqe1VmZl1/f0huf25IHWxGHX9ZM25GM31ZMX9uSHd3XX9/XXd3ZmaIiIBdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwYxQIBwSCSOAoJhoEg8ABDMoWeQiBIj1iHnOVwEqlaHkCFcCiUBxXCSbTMhbmc7QAcEAQA7)
(см. рис. 6.3)
Способ 5. Перепишем равносильную уравнению (1) систему (2) в виде
![](data:image/gif;base64,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)
Построив тогда в плоскости
![](data:image/gif;base64,R0lGODlhIQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAcAAwAhQAAAAAAAAAAHR0AAAAAMx0AMgAcSAAdSB0dSAAzWwAyWgAzWh1Ibh1GbDMAADQ0HTNbWzNZfzNdgDNbgEgcAEgdAFozAFszAFtIHUZGM1lZf1l/WV1/f0Rqe0huf1VmZmxGHW5IHX9ZM25GM3d3XX9/XX9uSHtqRGZmVXd3VXd3ZmaIiIBdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZtQIBwSCwaj8iiJcCMJJ/DwJAlhSarQ4sV6TBaCE+qIArACDxKcFSQMSoACSHlYHTEAZR7l2gaNIYDR1h3eEYURH5Fc0JqQgVFIwALQ3tDIGcAWkSTUFgWY0IXbwAOWABYFQEMUUxFVAEEGw5qQQA7)
график функции
![](data:image/gif;base64,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)
при условии
![](data:image/gif;base64,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)
(см. рис. 6.4), мы приходим к выводам, полученным ранее четырьмя рассмотренными способами.
Ответ: если
![](data:image/gif;base64,R0lGODlhLQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAoAAwAhQAAAAAAAAAAHR0AAAAAMx0AMgAdSB0dSB0dSR0zWwAzWwAzWgAyWh1Ibh1GbDMAADIAHTMAMzNbWzNZfzNbgEgcAFszAFozAFoyAEZGM1lZf1l/WV1/f0huf1VmZl13d25IHWxGHX9ZM3d3XX9/XXtqRH9uSGZmVXd3VXd3ZmaIiIBdM4BuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZmQIBwSCwaj8ikcpl8BALM6DIyJEivyw6W2NgmiKGAAGBIhrvYA7GiED6QFugW8LQCLkVKERPQw5+AT21CIAEOAHZCBUYDcnNDFUILkElxh48AFBZDTkyOWAhCdQAPiUkgUSuAZQBBADs=)
, то решений нет;
если
![](data:image/gif;base64,R0lGODlhLQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAoAAwAhQAAAAAAAAAAHQAAMx0AMgAdSB0dSB0dSR0zWwAzWwAzWgAyWh1GbDMAADIAHTMAMzNbWzNZfzNbgEgcAFszAFozAEZGM1lZf1l/WV1/f0huf1VmZl13d25IHWxGHX9ZM3d3XX9/XXtqRGZmVXd3VXd3ZmaIiIBdM4BuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZbQIBwSCwaj8ikcplsBALM6PIxHEivSw12W0QQPQEBoMBdGoiThLBRpDzfT7X0aQVUipKtGx4fdgIMAHVCBGVME0IKQ4hGfE9lEhRDToZMB0J0AA2DlUInb2QAQQA7)
, то
![](data:image/gif;base64,R0lGODlhIwATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAeAAwAhQAAAAAAAAAAHR0AAAAcSAAdSB0dSAAyWgAzWwAzWh1GbB1IbjMAADQ0HTNZf0gcAEgdAFszAFoyAERqe1VmZkhuf2xGHW5IHX9ZM25GM2ZmVX9/XX9uSHd3ZmaIiIBdM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZLQIBwSCwaj8ikUkhYOomMQPNJBUyrS8v1ExAMA9jhdXgAIIqRgHodOBfHAM5AESbCAY/6UFvMABJHbGtHd3pDEldgQhABC2FRXQBBADs=)
;
если
![](data:image/gif;base64,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)
, то
![](data:image/gif;base64,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)
;
если
![](data:image/gif;base64,R0lGODlhLwATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAqAAwAhQAAAAAAAAEAAAAAHR0AAAAeHgAAMx0AMgAdSB0dSQAdRwAAqgAzWgAzWwAyWB1GbDMAADNbWzFZfTNZfzNdgDNbgEgcAEccAUYcAEgeNFozAFgyAFszHVszAEZGM0hZf1lZf0hdgFl/WV1/f0huf1VmZm5IHWxGHX9ZM31ZMXd3XX9/XXtqRH9uSGZmVXd3VXd3ZmaIiIBdM4BdSIiIZqoAAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZmQIBwSCwaj8ikcsmEBAISppSZGQom0+yRNLRoG9okeHgKDACIYyBs9A4vDCFEGUizAYnhplhZEgxEGk+DT3FEXEKAQwdMBAV3Q4YAGH53D0MfHUNOSQEKd4SKT4AQikQykACEawBBADs=)
, то
![](data:image/gif;base64,R0lGODlhYAAtAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwBbACcAhQAAAAAAAAAAHR0AAAAAMx0AMgAdSB0dSB0dSQAzWgAzWx0zWwAyWh1GbB1IbjMAADMAHTMAMzQ0HTNbWzNZfzNbgDNdgEgcAEgdAEgeNEceM1ozAFszHVszAEZGM0hZf1lZf1l/WV1/f0huf1VmZlV3d113d0Rqe25IHWxGHX9ZM25GM39ZSHd3XX9/XXtqRGZmVXd3VX9uSHd3ZmaIiIBdM4BuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwb/QIBwSCwaj8ikcslsOp/QZmBKrVqvWGp0yzUGuuCwmPgdm8/SMno9fEzP6rA7vs4M6V08GEVgGy8JRxpQekmDShB+RRtjhV0vikUXSIdSXgIABoKRTwiNRJNCD1EoU32cHEUdWApFdGobrUKhQqtXsq6cKVxaQmoqp0IFYA2KKkuVR28AsIGzhkuMfipVwYS+Qx1tAROcW6VVuER2Sm9xpgAP1uPKU5reYsvw84SO9Pde9wGYvu/4/0RQANjl5QpAbwMOKjRCgVeWhxAjSpwoD4AEZ0RsWRG30IwDAAcArOh4r5QsDPZIqlzJsqVLMHMavuREjpnMmX5GDKGF0xvHHJ5seAL142loJJ1GkyoFUEzIh6WNqKyDusWKoiAAOw==)
.
Показательные и логарифмические неравенства с параметрами
Пример. Найти все значения параметра
, при которых неравенство ![](data:image/gif;base64,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)
выполняется для всех действительных значений
. Решение. Исходное неравенство
![](data:image/gif;base64,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)
равносильно следующей совокупности двух систем:
![](data:image/gif;base64,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)
В системе (1) параметр
, поэтому коэффициент
, стоящий при
в левой части последнего неравенства, положителен, следовательно, последнее неравенство системы (1) равносильно неравенству ![](data:image/gif;base64,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)
которое не может выполняться при всех действительных значениях
при любом фиксированном значении параметра
. Таким образом, система (1) не дает искомых значений параметра.В системе
(2)из первого неравенства (
) так же, как и раньше, вытекает, что
, следовательно, второе неравенство равносильно неравенству
,которое, очевидно, выполняется для всех действительных
тогда и только тогда, когда ![](data:image/gif;base64,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)
С учетом того, что
, получаем ![](data:image/gif;base64,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)
Ответ:
![](data:image/gif;base64,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)
Производная и ее применения
Пример. Найти все значения параметра
, при которых функция ![](data:image/gif;base64,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)
имеет хотя бы один экстремум строго между числами
и
. Решение. Для вычисления экстремумов функции
найдем её производную:
откуда следует, что в точках экстремума, то есть при
, значение параметра
, так как
. Поэтому интервал
, на котором, согласно условию задачи, надо искать экстремум, целиком расположен справа от точки 0.Дальнейшее решение задачи изложим двумя способами.
I- ый способ. Рассмотрим квадратный трехчлен
с абсциссой вершины
и дискриминантом
, положительность которого следует из того, что ![](data:image/gif;base64,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)
Если абсцисса
вершины параболы, являющейся графиком функции
, расположена левее интервала
, то есть величина
, то значения
и
должны быть разных знаков, причем
- отрицательно: