Question

if a-b=7 and a^2 + b^2=87 , then find the value of a^3 - b^3

Answer 1

let
a-b = 7 ....(1)

now
a^2 + b^2 = 87
you can write it this way

(a-b)^2 + 2ab = 87
put value (a-b)
49 + 2ab = 87
ab = 19 ...(2)

and
a^2 + b^2 = 87 ....(3)

then
a^3 - b^3 = (a-b) ( a^2 + b^2 + ab)

put its value from equation (1), (2) , & (3)
= 7×(87 +19)
= 7×106
= 742

## hope it can help you ##