Question

If x+1/x=5, find the value of x³+1/x³

Answer 1

Step-by-step explanation:

x³+1/x³=(x+1/x)(x^2+1/x^2-1).....eq(1)

We have,

x+1/x=5

(x+1/x)^2=25

x^2+1/x^2+2=25

x^2+1/x^2=23

Now,

Putting the values in eq 1

(x+1/x)(x^2+1/x^2-1)

=(5)(23-1)

=5*22

=110

Therefore x³+1/x³ = 110