Question

If x = 3+2 root 2 then find x- 1/x​

Answer 1

We know that:

x = 3 + 2*√2

And we want to find the value of:

`x - (1)/(x)`

First, we can rewrite the above expression as:

`x - (1)/(x) = (x^2)/(x) - (1)/(x) = (x^2 - 1)/(x)`

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

`(x^2 - 1)/(x) = ((3 + 2*√(2))^2 - 1 )/(3 + 2*√(2) ) = (3^2 + 2*2*√(2) + (2*√(2))^2 - 1 )/(3 + 2*√(2) )`

Now we can simplify this to get:

`(9 + 4*√(2) + 4*2 - 1 )/(3 + 2*√(2) ) = (16 + 4*√(2) )/(3 + 2*√(2) )`

We could finally compute that last equation, to get:

`(9 + 4*√(2) + 4*2 - 1 )/(3 + 2*√(2) ) = (16 + 4*√(2) )/(3 + 2*√(2) ) = 3.716`