x²+3x-7=0 ,если x1 и x2 -корни ур-ия, то сумма x1^4+ x2^4 =. Created by DrMartens. algebra-ru

по теореме Виетаотсюдаответ: 431

x²+3x-7=0 ,если x1 и x2 -корни ур-ия, то сумма x1^4+ x2^4 =...

DrMartens @DrMartens

July 2022 1 7 Report

x²+3x-7=0 ,если x1 и x2 -корни ур-ия, то сумма x1^4+ x2^4 =

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dtnth

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$x^2+3x-7=0$
по теореме Виета
$x_1+x_2=-3$
$x_1x_2=-7$
отсюда
$x^4_1+x^4_2=\\\\(x^2_1+x^2_2)^2-2x^2_1x^2_2=((x_1+x_2)^2-2x_1x_2)^2-2(x_1x_2)^2=\\\\((-3)^2-2*(-7))^2-2*(-7)^2=\\\\(9+14)^2-2*49=\\\\23^2-98=529-98=431$
ответ: 431

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