If 5x + 9y = 5 and 125x³ + 729y3 = 120 then the vlaue

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

1. 1/9
2. 1/135
3. 45
4. 135

Correct Option: B

5x + 9y = 5
On cubing both sides, (5x)³ + (9y)³ + 3 × 5x × 9y (5x + 9y) = (5)³
[∵ (a + b)³ = a³ + b³ + 3ab (a + b)]
⇒ 125x³ + 729y³ + 135xy × 5 = 125
⇒ 120 + 135 × 5xy = 125
⇒ 135 × 5xy = 125 – 120 = 5

⇒ xy =	5	=	1
	135 × 5		135