solve this please
it's little urgent!
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Answer:
(p⁴/q²) - (4p²/q) + 2
Step-by-step explanation:
Given Equation is x² - px + Q.
Here, a = 1, b = -p, c = q.
Given that α,β are the roots of the equation.
(i)
Sum of roots = -b/a
α + β = -(-p)/1
α + β = p.
(ii)
Product of roots = c/a
αβ = q/1
αβ = q.
LHS:
(α²/β²) + (β²/α²)
= [(α² + β²)² - 2α²β²]/α²β²
= {[(α+β)² - 2αβ]² - 2(αβ)}²}/(αβ)²
= {[(p)² -2(q)]²-2(q)²}/(q)²
= [(p² - 2q)² - 2(q)²]/q²
= [(p⁴ + 4q² - 4p²q - 2q²)]/q²
= [(p⁴ - 4p²q + 2q²)]/q²
= (p⁴/q²) - (4p²q/q²) + (2q²/q²)
= (p⁴/q²) - (4p²/q) + 2.
Hope it helps!