Question

if x+1/x=√2 ,then x^2+1/x^2=​

Answer 1

Answer:

x+1/x=2

As we know that

(a+b)²=a²+b²+2ab

(x+1/x)²=(2)²

x²+1/x²+2=4

x²+1/x²=4-2

x²+1x²=2

Step-by-step explanation:

Answer 2

The value of $x^{2}+\frac{1}{x^{2}}$ is 0.

Step-by-step explanation:

The expansion of (a + b)² is:

(a + b)² = a² + 2ab + b²

It is provided that:

$x+\frac{1}{x}=\sqrt{2}$

Compute the value of $x^{2}+\frac{1}{x^{2}}$ as follows:

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

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

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

                     $x^{2}+\frac{1}{x^{2}}=0$

Thus, the value of $x^{2}+\frac{1}{x^{2}}$ is 0.

Learn more:

https://brainly.in/question/12150873