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Conjugate of a Complex Number

If x+y+z=0,...

Question

If $x + y + z = 0,$ what will be the value of $\frac{x^{2} + y^{2} + z^{2}}{- (x y + y z + z x)} ?$

A

4

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B

6

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C

2

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D

8

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Solution

The correct option is C $2$
Given $x + y + z = 0$

$⟹ x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 z x = 0$

$⟹ x^{2} + y^{2} + z^{2} = - 2 (x y + y z + z x)$

$∴ \frac{x^{2} + y^{2} + z^{2}}{- (x y + y z + z x)} = 2$

Hence, the answer is $2$ .

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