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If 5x + 9y = 5 and 125x3 + 729y3 = 120, then the value of the product of x and y is?
Answer & Solution
Correct Answer:
Option
C
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 = $$\frac{1}{{135}}$$
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 = $$\frac{1}{{135}}$$
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