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If $x^{2} + y^{2} + z^{2} - x y - yz - z x = 0$ and $x = 5$ , find $x + y + z (x, y, z$ real).

Competition practiceAlgebra

A5
B15
C25
D125

Step-by-Step Solution

The expression is

\frac{1}{2} [(x - y)^{2} + (y - z)^{2} + (z - x)^{2}] = 0

, so

x = y = z = 5

and the sum is 15.

Answer: B) 15

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