{x^2 +y^2 -2z^2 =2a^2
{z^2 -xy =a^2 <=> 2z^2 -2xy =2a^2
x^2 +y^2 -2z^2 = 2z^2 -2xy <=> x^2 +2xy +y^2 =4z^2 <=> (x+y)^2 = (2z)^2 <=> |x+y|=|2z|
[x+y=2z
[x+y= -2z
1)
{x+y=2z
{x+y+2z =4(a^2 +1)
2z+2z =4(a^2 +1) <=> 4z=4(a^2 +1) <=> z=a^2 +1 <=> z -a^2 =1
2)
{x+y = -2z
{-2z+2z = 4(a^2 +1)
4(a^2 +1)=0, но a^2 +1 >1.
x+y +z -3a^2 = 2z +z -3a^2 = 3(z -a^2) = 3