Question

If x= √5+2 then find the value of x-1/x​

Answer 1

Answer:

The answer is 4.

Step-by-step explanation:

$x=\sqrt5+2$

We have to find the value of $x-\frac{1}{x}$

Simplifying $x-\frac{1}{x}$ ,

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

Putting the value of x in the above equation,

$x-\frac{1}{x}=\frac{(\sqrt5+2)^2-1}{\sqrt5+2}$

$=\frac{(5+4\sqrt5+4)-1}{\sqrt5+2}$

$=\frac{4\sqrt5+8}{\sqrt5+2}$

Rationalizing the denominator,

$=\frac{4\sqrt5+8}{\sqrt5+2}*\frac{\sqrt5-2}{\sqrt5-2}$

$=\frac{4(\sqrt5+2)(\sqrt5-2)}{(\sqrt5+2)(\sqrt5-2)}$

$=4$

Hence, the answer is 4.

Hope it helps you.