If x2 + 4y2 = 17 and xy = 2, where x> 0, y > 0, then what is the value of x3 + 8y3?
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 65
x2 + 4y2 = 17.
On adding 4xy on both sides we get,
x2 + 4y2 + 4xy = 17 + 4xy
(x + 2y)2 = 17 + 8 = 25
x + 2y = 5...........(1)
On cubing both sides we get,
x3 + 8y3 + 3 × x × 2y(x + 2y) = 125
x3 + 8y3 = 125 - 60 = 65.