If x + 2y = 19 and $x^3 + 8y^3 = 361,$ then xy is equal to :
Answer & explanation
Correct answer: option 1
We know that,
(a + b)3 = a3 + b3 + 3ab(a + b)
Given,
x + 2y = 19
x3 + 8y3 = 361
According to the question,
(x + 2y)3 = x3 + 8y3 + 6xy(x + 2y)
= (19)3 = 361 + 6xy × 19
= 6859 = 361 + 114xy
= 114xy = (6859 – 361)
= 114xy = 6498
= xy = 57