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 !.