If alpha and beta are the roots of x square+x-2=0,find the value of (1÷alpha square...

If alpha and beta are the roots of x square+x-2=0,find the value of (1÷alpha square +1÷beta square?

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Answers (2)

ROBERT
8 months ago
Good evening.

x² + x - 2= 0
ax² + bx + c= 0

a= 1, b= 1; c= -2.

Let alpha= A; beta= B.

Sum= A + B= -b/a= -1/1= -1

Product= AB= c/a= -2/1= -2

(1/A² + 1/B²)= ?
(B² + A²)/(A²B²)
((A + B)² - 2AB)/(AB)²
((-1)² - 2(-2))/(-2)²
(1 + 4)/4
5/4

Thus, (1/A² + 1/B²)= 5/4.

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