Question

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

Answer 1

Explanation:

Answer 2

`(5)/(4)`

Explanation:

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

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

α + β = -
`(b)/(a)` = - 1 and αβ =
`(c)/(a)` = - 2, then

`(1)/(\alpha ^2)` +
`(1)/(\beta^2 )`

=
`(\beta^2+\alpha^2  )/(\alpha ^2\beta^2 )`

=
`((\alpha +\beta )^2-2\alpha \beta )/(\alpha ^2\beta^2 )`

=
`((-1)^2-2(-2))/((-2)^2)`

=
`(1+4)/(4)`

=
`(5)/(4)`