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Question
If x + 2y = 5, then show that x3 + 8y3 + 30xy = 125.
Sum
Solution
Given x + 2y = 5
(x + 2y)3 = 53
⇒ (x)3 + (2y) + 3(x)(2y)(x + 2y) = 53 ....[Using (a + b)3 = (a)3 + (b)3 + 3ab (a + b)]
⇒ (x)3 + (2y)3 + 6xy(x + 2y) = 125
⇒ (x)3 + (2y)3 + 6xy(5) = 125
⇒ x3 + 8y3 + 30xy = 125.
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