If 5x + 9y = 5 and 125x³ + 729y³ = 120, then the value of the product of x and y is?

Solution (By Examveda Team)

5x + 9y = 5 . . . . . (i)
125x³ + 729y³ = 120 . . . . . (ii)
From equation (i) cubing both sides
⇒ (5x + 9y)³ = 5³
⇒ 125x³ + 729y³ + 3 × 5x × 9y(5x + 9y) = 125
⇒ 125x³ + 729y³ + 135xy × 5 = 125
⇒ 120 + 135xy × 5 = 125
⇒ 135xy × 5 = 5
⇒ xy = $$\frac{1}{{135}}$$
∴ product of x & y = $$\frac{1}{{135}}$$