Question

if x+1/x=5,then findthe value of x²+1/x²​

Answer 1

The value of $x^{2}+\frac{1}{x^{2}}$ is 23.

Step-by-step explanation:

Th expansion of (a + b)² is:

(a + b)² = a² +2ab + b²

It is provided that:

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

Use the above mentioned identity to compute the value of $x^{2}+\frac{1}{x^{2}}$ as follows:

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

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

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

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

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

Thus, the value of $x^{2}+\frac{1}{x^{2}}$ is 23.

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