If 2x + 3y = 16 and xy = 9, then find 8x3 + 27y3.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 1504.
Given that, 2x + 3y = 16 ...(i)
And xy = 9
(a + b)3 = a3 + b3 + 3ab(a + b)
According to the given question,
Taking cube on both the sides of equation(i),
(2x + 3y)3 = (2x)3 + (3y)3 + 3(2x)(3y)(2x + 3y)
⇒ 163 = 8x3 + 27y3 + 18(9)(16)
⇒ 8x3 + 27y3 = 4096 - 2592
⇒ 8x3 + 27y3 = 1504
Hence the required answer is 1504.