If $x - y = 4 $ and $x^3 - y^3 = 316 $, then the value of $x^4 + y^4 $ is :
Answer & explanation
Correct answer: option 2
x - y = 4
x3 – y3 = 316
We know that,
x3 – y3 = (x - y)[(x - y)2 + 3xy]
= 316 = 4[(x - y)2 + 3xy]
= 79 = [16 + 3xy]
= 63 = 3xy
= xy = 21
= x = 7
then, y = 3
x4 + y4 = 74 + 34 = 2482