Question

if x²+(1/x²)=23,then find the value of x+(1/x),x³+(1/x³)​

Answer 1

Explanation:

x²+(1/x²)=23 ---------(1)

x²+(1/x²)+2 = 23+2

(x+1/x)²  = 25

x+1/x = 5 ---------(2)

or x+1/x = -5 ----(3)

(1)*(2) : calculate...

x^{3}+x+(1/x)+1/x^{3} = 115

x³+(1/x³)​+5                =115

x³+(1/x³)                    = 110

In the same melody

(1)*(3) : x³+(1/x³)        = -110

Answer x+(1/x) = 5 x³+(1/x³)​ = 110

             x+(1/x) = -5 x³+(1/x³)​ = -110