Mathematics: If alpha and beta are the root of equation x^2+x-2=0 find the value of 1/alpha^2+1/beta^2

2Step-by-step explanation:edge 2020...

If alpha and beta are the root of equation x^2+x-2=0

bthakkar25

14.01.2022

$\frac{5}{4}$

Step-by-step explanation:

Given that α and β are the roots of x² + x - 2 = 0

with a = 1, b = 1, c = - 2, then

α + β = - $\frac{b}{a}$ = - 1 and αβ = $\frac{c}{a}$ = - 2, then

$\frac{1}{\alpha ^2}$ + $\frac{1}{\beta^2 }$

= $\frac{\beta^2+\alpha^2 }{\alpha ^2\beta^2 }$

= $\frac{(\alpha +\beta )^2-2\alpha \beta }{\alpha ^2\beta^2 }$

= $\frac{(-1)^2-2(-2)}{(-2)^2}$

= $\frac{1+4}{4}$

= $\frac{5}{4}$

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AshtinDCardwell14

20.05.2021

Step-by-step explanation:

edge 2020

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