Question

If x=root 2-1 find x+1/x​

Answer 1

Answer:

(√2+1)^2+1/√2+1

2+1+4+1/√2+1

8/√2+1 ×√2-1/√2-1

8√2+8/2-1

8√2+8

is your answer

Answer 2

Answer:

The final answer we get here is:

$2 \sqrt{2}$

Step-by-step explanation:

We have been given the value,

$x = \sqrt{2} - 1$

Then the inverse of x must give,

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

Rationalizing the term by multiplying the term with,

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

Doing that gives,

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

Adding both gives,

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

And Tada your answer.