Question

Given that,

Answer 1

Answer:

The answer is 23.

Explanation:

You square the 1st expression and you will get the 2nd expression :

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

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

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

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

Answer 2

Answer:

$23$

Explanation:

Use: $(a+b)^2= a^2+2 ab+b^2$

Square both sides:

$\Big( x+\frac{1}{x}\Big)^2=5^2\\\implies x^2+2(x) \Big(\frac{1}{x}\Big) +\frac{1}{x^2}=25\\\implies x^2+\frac{1}{x^2}=25-2=\boxed {\color{red}{23}}$