Question

If x =3+2 root 2 find x - 1/x​

Answer 1

`x-\frac 1x\\\\\\=3+2\sqrt 2- \frac 1{3+2\sqrt 2}\\\\\\=3+2\sqrt 2 - (3-2\sqrt2)/(\left(3+2\sqrt 2\right) \left(3-2\sqrt 2 \right))\\\\\\=3+2\sqrt 2 -(3-2\sqrt 2)/(3^2 - \left(2\sqrt 2 \right)^2)\\ \\\\=3+2\sqrt 2-(3-2\sqrt2)/(9-8)\\\\\\=3+2\sqrt 2-3+2\sqrt 2\\\\\\=4\sqrt2`

Answer 2

-2+2
`√(2)`

Explanation:

Since we have the value of x, 3+2
`√(2)`, we can plug that value into the new equation.

We would recieve (3+2
`√(2)`-1)/3+2
`√(2)`

Which could simplify to -2+2
`√(2)`