PRMo 2013 - 3 real numbers x,y,z are such that


11. Three real numbers x,y,zx, y, z are such that
x2+6y=−17x^2 + 6y = -17,
y2+4z=1y^2 + 4z = 1, and
z2+2x=2z^2 + 2x = 2.

What is the value of x2+y2+z2x^2 + y^2 + z^2?

Solution:

Add all LHS and RHS and make whole squares of x,y,z
You will get:

(x + 1)^2 + (y+3)^2 + (z+2)^2 = 0
So each term is 0.
That gives you the exact values of x,y,z.

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