Question

If x =3+2 root 2 find x - 1/x​

Answer 1

Answer:

-2+2$\sqrt{2}$

Step-by-step explanation:

Since we have the value of x, 3+2$\sqrt{2}$, we can plug that value into the new equation.

We would recieve (3+2$\sqrt{2}$-1)/3+2$\sqrt{2}$

Which could simplify to -2+2$\sqrt{2}$

Answer 2

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