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Algebra of Complex Numbers

If x, y and z...

Question

If x, y and z are real number such that $x^{2} + y^{2} + 2 z^{2} = 4 x - 2 z + 2 y z - 5$ then the possible value of (x-y-z) is

A

0

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B

1

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C

4

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D

-1

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Solution

The correct option is A 0
$x^{2} + y^{2} + 2 z^{2} = 4 x - 2 z + 2 y z - 5$
$⟹ (x^{2} - 4 x + 4) + (y^{2} - 2 y z + z^{2}) + (z^{2} + 2 z + 1) = 0$
$⟹ (x - 2)^{2} + (y - z)^{2} + (z + 1)^{2} = 0$
$⟹ x = 2, y = z, z = - 1$
$x - y - z = 2 + 1 + 1 = 4$

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