If x3 + y3 = 16 and x + y = 4, then the value of x4 + y4 is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 32
⇒ x3 + y3 = 16
⇒ (x + y)(x2 + y2 - xy) = 16
⇒ 4(x2 + y2 - xy) = 16
⇒ x2 + y2 - xy = 4 ...(1)
⇒ (x + y)2 = 16
⇒ x2 + y2 + 2xy = 16 ...(2)
By (1) & (2) we got
⇒ xy = 4 & x2 + y2 = 8
⇒ x4 + y4 = (x2 + y2)2 - 2x2y2
⇒ x4 + y4 = 64 - 2 × 16
⇒ 64 - 32 = 32