Question

If (x+ 1/x) = 5, find the value of (x^2 + 1/x^2) and (x^4 + 1/x^4).​

Answer 1

x+1/x=5

squaring on both sides

(x+1/x)²=5²

x²+1/x²+2(x)(1/x)=25

x²+1/x²+2=25

x²+1/x²=25-2

x²+1/x²=23

again squaring on both sides

(x²+1/x²)²=23²

x⁴+1/x⁴+2(x²)(1/x²)=529

x⁴+1/x⁴+2=529

x⁴+1/x⁴=529-2

x⁴+1/x⁴=527