х2...

July 2022 1 9 Report

х1 и х2 корни квадратного уравнения х2 - 5х - 2 = 0. Не решаючи уравнение, найдите значение выражения: 1/х1 + 1/х2

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fadarm

Verified answer

$\frac{1}{ x_{1} }+ \frac{1}{ x_{2} }= \frac{ x_{1}+x_{2} }{x_{1}*x_{2}}$
По теореме Виета
$x_{1}+x_{2}=-p=5$
$x_{1}*x_{2}=q=-2$
$\frac{ x_{1}+x_{2} }{x_{1}*x_{2}}= \frac{5}{-2}=-2,5$

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