please answer the following questions
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(i) x²-px+q =0 ( α+β=p, αβ=q)
α²/β²+β²/α² = α⁴+β⁴/α²β²
= [(α²+β²)² - 2α²β²] ÷ α²β² = { [ ( α+β)² - 2αβ ]²-2α²β² } ÷ α²β²
={ [p²-2q]² - 2q²} ÷ q² = (p⁴ + 4q⁴-4p²q²-2q²) ÷q²
=
(ii) α/β + β/α = (α²+β²)÷αβ =[ ( α+β)² -2αβ] ÷ αβ
= (p²-2q²) ÷ q
Anonymous:
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