Question

if x+ 1/x= 5 , then find the value of x^2 + 1/x^2​

Answer 1

Question:

If x+ 1/x= 5 , then find the value of x^2 + 1/x^2.

Answer:

x+1/x=5

squaring on both sides

(x+1/x)²=(5)²

using identity: (a+b)²=a²+2ab+b²

x²+2(x)(1/x)+1/x²=25

x²+2+1/x²=25

x²+1/x²=25-2

x²+1/x²=23

therefore, final answer:

x²+1/x²=23

Answer 2

$\: if \: x + 1/x = 5 , find \: the \: value \: of \: {x}^{2} + 1/ {x}^{2}$

$given$

$( x + 1 /x ) = 5$

We need to find x² + 1 /x²

( x + 1 / x )² = 25

= x²+ 1 / x² + 2 (x)(1/x) = 25

= x²+ 1/x² + 2 = 25

= x²+ 1 / x² = 25 – 2

= x² + 1 / x² =23

Hence x² + 1 / x² = 23