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Question

If fx=64x3+1x3and α, β are the roots of 4x+1x=3. Then,
(a) f(α) = f(β) = −9
(b) f(α) = f(β) = 63
(c) f(α) ≠ f(β)
(d) none of these

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Solution

(a) fα=fβ=-9

Given:
fx=64x3+1x3
fx=4x+1x16x2+1x2-4
fx=4x+1x4x+1x2-12

fα=4α+1α4α+1α2-12 and fβ=4β+1β4β+1β2-12
Since α and β are the roots of 4x+1x=3,
4α+1α=3 and 4β+1β=3
fα=332-12=-9 and fβ=332-12=-9
fα=fβ=-9

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