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Question

if x +y+ 4 =0 , then find the value of x3  +  b3  - 12xy + 64


Solution

Given (x + y + 4) = 0
⇒ x + y = –4  → (1)
Cubing on both the sides, we get
(x + y)3 = –43
⇒ x3 + y3 + 3xy(x + y) = –64
⇒ x3 + y3 + 3xy(–4 ) = –64   [From equation (1)]
⇒ x3 + y3 –12xy + 64 = 0

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