Question

If x^2-y^2=15 and x+y=3, find the value of (x-y)^3.

Answer 1

ANSWER

Given:

x²-y²=15

x+y=3

To find:

(x-y)³

Answer:

x²-y²=15

=>(x+y)(x-y)=15

=>3(x-y)=15 [Given x+y=3]---------(i)

=> (x-y)=5---------(ii)

Adding (i) and (ii)

2x=8

=> x=4

Put in (ii)

4-y=5

=>y=-1

(x-y)³=x³-y³-3xy(x-y)

=64+1+12(5)

=65+60

=125

Ans. = 125