If $x-y=4$ and $x^3-y^3=316, y>0$ then the value of $x^4-y^4$ is:
Answer & explanation
Correct answer: option 2
Given,
x - y = 4
x3 – y3 = 316
We know,
x3 – y3 = (x - y)[(x - y)2 + 3xy]
x3 – y3 = (x - y)[(x - y)2 + 3xy]
= 316 = 4[(x - y)2 + 3xy]
= 79 = [16 + 3xy]
= 63 = 3xy
= xy = 21
So, x = 7
y = 3
x4 - y4 = 74 - 34 = 2320