Question

If x+1/x=5 then evaluate x^2+1/x^2 and x^4+1/x^4​

Answer 1

Step-by-step explanation:

Given,

x+1/x=5,

Now,By sq. both side, we get:

(x+1/x)²=5²

x²+1/x²+2*x*1/x=25 [ x*1/x= 1]

x²+1/x²=25-2

x²+1/x²=23{Ans}

Now, second one:

Similarly,by sq. both sides, we get:

(x²+1/x²)²=23²

x^4+1/x^4+2*x²*1/x²=529

x^4+1/x^4=529-2 [ x²*1/x²= 1]

x^4+1/x^4=529{Ans}

Hope it's beneficial for you.