Question

if X+1/X =5 then find X^2 -1/X^2, X^3+1/X^3 and X^5 +1/X^5​

Answer 1

Step-by-step explanation:

Given x+1/x=5

Cubing on both sides,

x^3 +1/x^3 + 3(x+1/x) = 125

Hence x^3+1/x^3=125-3(5)=125-15=110

Squaring on both sides,

x^2+1/x^2=25-2=23

Hence x^5+1/x^5=(x^2+1/x^2)(x^3+1/x^3) =125×23=2875