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

Square 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, square 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

I hope this will help you