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8 months ago
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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