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Question

If α and β are the roots of the equation x26x+8=0, then find the values of
(i) α2+β2 (ii) 1/α+1/β (iii) αβ(α>β)

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Solution

From the given equation we get α+β=6 and αβ=8
(i) α2+β2=(α+β)22αβ=(6)22(8)=20
(ii) 1α+1β=α+βαβ=68=34
(iii) (αβ)2=(α+β)24αβ
(αβ)=±(α+β)24αβ=624(8)
(αβ)=±2
αβ=2(α>β)

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