Question

If x + 2y = 5, then show that x³ + 8y³ + 30xy = 125.

Answer 1

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.