Question

x^2+6y=-17 y^2+4z =1 z^2+2x=2 find x^2+y^2+z^2

Answer 1

Add the three equations, we get

x2 + 2x + y2 + 6y + z2 + 4z = -14

x2 + 2x + 1 +  y2 + 6y + 9 + z2 + 4z + 4 = 0

( x + 1 )2 + ( y + 3 )2 + ( z + 2 )2 = 0

x = -1 , y = -3 , z = -2

x2 + y2 + z2 = 14