Answer:
[tex]\frac{5}{4}[/tex]
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 = - [tex]\frac{b}{a}[/tex] = - 1 and αβ = [tex]\frac{c}{a}[/tex] = - 2, then
[tex]\frac{1}{\alpha ^2}[/tex] + [tex]\frac{1}{\beta^2 }[/tex]
= [tex]\frac{\beta^2+\alpha^2 }{\alpha ^2\beta^2 }[/tex]
= [tex]\frac{(\alpha +\beta )^2-2\alpha \beta }{\alpha ^2\beta^2 }[/tex]
= [tex]\frac{(-1)^2-2(-2)}{(-2)^2}[/tex]
= [tex]\frac{1+4}{4}[/tex]
= [tex]\frac{5}{4}[/tex]
