Question #9cf7b

1 Answer
Feb 23, 2015

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 !.