If x2 + 9y2 = 40 and xy = 4, where x > 0, y > 0, then what is the value of (x3 + 27y3)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 224.
(x + 3y)2 = x2 + 6xy + 9y2
= (x2 + 9y2) + 6xy
= 40 + 6 × 4 = 64
⇒ x + 3y = 8
x3 + 27y3 = (x + 3y)(x2 - 3xy + 9y2)
= 8(40 - 3 × 4)
= 8 × 28
= 224