Question

X + 1/ X = 5 then X^2 + 1 / x^2 = ?​

Answer 1

Answer:

$({x + \frac{1}{x} })^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x}$

${5}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2$

$25 - 2 = {x}^{2} + \frac{1}{ {x}^{2} }$

$23 = {x}^{2} + \frac{1}{ {x}^{2} }$

Answer 2

Answer: 23

Step-by-step explanation:

See this, and always remember this:

$(x+\frac{1}{x} )^2 = x^2 + 2*x*\frac{1}{x} + \frac{1}{x^2}$

$(x+\frac{1}{x} )^2 = x^2 +\frac{1}{x^2} +2$

so putting X + 1/X = 5 in above equation

$5^2 = x^2 +\frac{1}{x^2} +2\\\\25 -2 = x^2 +\frac{1}{x^2}\\\\ x^2 +\frac{1}{x^2} = 23$

Extra tip : if it is x-1/x , then

$(x-\frac{1}{x} )^{2} = x^2+\frac{1}{x^2} -2$