Question

if x+(1/x)=5, find x³-y³​

Answer 1

Given,

x+1/x = 5

To find: x^3-1/x^3 =?

from the identity, x^3-y^3=(x-y)(x^2+xy+y^2)

» x^3-1/x^3 = (x-1/x)(x^2+x.1/x +1/x^2)

or, x^3-1/x^3 = 5(x^2+1/x^2+1)

or,x^3-1/x^3 = 5([x+1/x]^2- 2x.1/x+1)

or,x^3-1/x^3 = 5(5^2 -2+1)

or,x^3-1/x^3 =5(25-1)

or,x^3-1/x^3 = 5(24)

or,x^3-1/x^3 = 120