Question

If x^2+1/x^2=18 then find the value of x^3-1/x^3

Answer 1

x^2+ 1/x^2=18
x^2+1/x^2 -2=18-2
(x-1/x)^2=1886
(x-1/x)=4

x^3-1/x^3
=(x-1/x)(x^2+1/x^2+2)
=4×(18+2)
=4×20
=80

Answer 2

x² + 1/x² = 18.
x² + 1/x² - 2 = 18 - 2.
(x-1/x)² = 1886.
(x-1/x) = 4.
After That,
x³ - 1/x³.
= (x-1/x)(x²+1/x²+2).
= 4×(18+2).
= 4×20.
= 80.