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Properties of Conjugate of a Complex Number

The value of ...

Question

The value of $x + y + z$ if $x^{2} + y^{2} + z^{2} = 18$ and $x y + y z + z x = 9$ is

A

9

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B

3

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C

6

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D

8

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Solution

The correct option is C $6$
Squaring both sides
$(x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2 (x y + y z + z x)$
we can substitute given values
$(x + y + z)^{2} = 18 + (2 \times 9)$
$(x + y + z)^{2} = 36$
$(x + y + z) = 6$

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