Question

Question #9cf7b

Answer 1

Hello,

Answer.

• `x = 2-2 sqrt(2)` and `y = 6 - 4 sqrt(2)`

or

• `x = 2+2 sqrt(2)` and `y = 6 + 4 sqrt(2)`.

Explanation

You have to solve `2x+2=x^2-2`, so `x^2-2x-4=0`.

Remark that `(x-2)^2=x^2-2x+4`, therefore :
`x^2-2x-4 = (x-2)^2-8`.

So, you have to solve `(x-2)^2=8`.
Solutions are `x-2 = \pm sqrt(8) = pm 2sqrt(2)`, it means
`x = 2 - 2 sqrt(2)` or `x=2+2 sqrt(2)`.

Finally, calculate corresponding `y` for each value of `x` : because `y = 2x+2`, it's easy !.