tex]...

August 2022 1 8 Report

Пусть x₁ и x₂ корни уравнения x²-15x+56 = 0
Не решая уравнения, найти значение выражения
[tex]\frac{x_{1} }{x_{2} } + \frac{x_2}{x_1}[/tex]

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Universalka

Verified answer

x² - 15x + 56 = 0

x₁ + x₂ = 15

x₁ * x₂ = 56

$\frac{x_{1}}{x_{2} }+\frac{x_{2}}{x_{1}}=\frac{x_{1}^{2}+x_{2}^{2}}{x_{1}*x_{2}}=\frac{(x_{1}+x_{2})^{2}-2x_{1}*x_{2}}{x_{1} *x_{2}}=\frac{15^{2}-2*56 }{56}=\frac{225-112}{56}=\frac{113}{56}=2\frac{1}{56}$

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