Задача 62246 Если 1 x и 2 x корни уравнения...

61bcd0862c9acd5f8803ecec

17.12.2021 21:06:50

Если 1 x и 2 x корни уравнения

5f3ea7e3faf909182968ddd9

17.12.2021 23:00:47

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По теореме Виета

x_(1)+x_(2)=7

x_(2)*x_(2)=-9



x^3_(1)+x^3_(2)=(x_(1)+x_(2))^3-3x^2_(1)x_(2)-3x_(1)x^2_(2)

x^3_(1)+x^3_(2)=(x_(1)+x_(2))^3-3x_91)*x_(2)*(x_(1)+x_(2))=

x^3_(1)+x^3_(2)=7^3-3*(-9)*7=7*(7^2+27)

x^3_(1)+x^3_(2)=7*76

x^3_(1)+x^3_(2)==532


(x^3_(1)+x^3_(2))/(3x_(1)*x_(2)=532/3*(-9)=[b]-532/27[/b]