Hi1315
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Given that,
[tex]x + \frac{1}{x} = 5[/tex]
so now find the value of
[tex] {x}^{2} + \frac{1}{ {x}^{2} } [/tex]
need step by step explanation.will give the brainliest​

Respuesta :

Lightx

Answer:

[tex] 23[/tex]

Explanation:

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

Square both sides:

[tex] \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}}[/tex]

CHERLYNnotCHERRY

Answer:

The answer is 23.

Explanation:

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

[tex] {(x + \frac{1}{x}) }^{2} = {5}^{2} [/tex]

[tex] {x}^{2} + 2(x)( \frac{1}{x}) + { (\frac{1}{x}) }^{2} = 25 [/tex]

[tex] {x}^{2} + 2 + \frac{1}{{x}^{2}} = 25 [/tex]

[tex] {x}^{2} + \frac{1}{{x}^{2}} = 23 [/tex]

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