Question 89877
{{{x^2+(highlight(x))^2=4}}} Plug in y=x


{{{2x^2=4}}} Combine like terms



{{{x^2=2}}} Divide both sides by 2


{{{x=0+-sqrt(2)}}} Take the square root of both sides


So our solutions are ({{{-sqrt(2)}}},{{{-sqrt(2)}}}) and ({{{sqrt(2)}}},{{{sqrt(2)}}})



Check:

{{{(sqrt(2))^2+((sqrt(2)))^2=4}}}


{{{2+2=4}}}


{{{4=4}}} works


or 


{{{(-sqrt(2))^2+((-sqrt(2)))^2=4}}}


{{{2+2=4}}}


{{{4=4}}} works




We can also verify with this graph


{{{drawing(500,500,-6,6,-6,6,
graph(500,500,-6,6,-6,6,x),
circle(0,0,2),
circle(sqrt(2),sqrt(2),0.05),
circle(sqrt(2),sqrt(2),0.08),
circle(-sqrt(2),-sqrt(2),0.05),
circle(-sqrt(2),-sqrt(2),0.08)

)}}}


and if you used Pythagoreans theorem, you would verify your answer.