Question

if x+1/x=4 find the value of x³+1/x³ , x-1/x , x³ - 1 / x³​

Answer 1

Answer:

x+1/x=4

=> (x+1/x)^2=4^2

=> (x-1/x)^2+4.x.1/x=16

=> (x-1/x)^2=16-4

=> (x-1/x)^2=12

=> (x-1/x)=√12

=> x-1/x=2√3

x^3+1/x^3

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

=4^3-3.4

=64-12

=52

x^3-1/x^3

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

=(2√3)^3+3.2√3

=8.3√3+6√3

=24√3+6√3

=30√3