Q1
ArithmeticAlgebra, Equations & Operations
If $x, y, z$ are real and $(x - 2)^2 + x^2 + y^2 + 2z^2 - 2yz - 2xz = 0$; then the value of $(x + y + z)$ is
- a.2
- b.8
- c.6
- d.10
Answer: (C) 6
Regroup the left side as $(x - 2)^2 + (x - z)^2 + (y - z)^2 = 0$. A sum of squares of real numbers is zero only when each square is zero, so $x = 2$, $z = x = 2$ and $y = z = 2$, giving $x + y + z = 6$. The values 2, 8 and 10 do not satisfy all three conditions.