Question

If x = 3+2 root 2 then find x- 1/x​

Answer 1

Answer:

We know that:

x = 3 + 2*√2

And we want to find the value of:

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

First, we can rewrite the above expression as:

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

Now we can replace the value of x by  the one above, we will get:

$\frac{x^2 - 1}{x} = \frac{(3 + 2*\sqrt{2})^2 - 1 }{3 + 2*\sqrt{2} } = \frac{3^2 + 2*2*\sqrt{2} + (2*\sqrt{2})^2 - 1 }{3 + 2*\sqrt{2} }$

Now we can simplify this to get:

$\frac{9 + 4*\sqrt{2} + 4*2 - 1 }{3 + 2*\sqrt{2} } = \frac{16 + 4*\sqrt{2} }{3 + 2*\sqrt{2} }$

We could finally compute that last equation, to get:

$\frac{9 + 4*\sqrt{2} + 4*2 - 1 }{3 + 2*\sqrt{2} } = \frac{16 + 4*\sqrt{2} }{3 + 2*\sqrt{2} } = 3.716$