ABC26GN0996 · Simplification

Subject: General Aptitude · Chapter: Simplification · Exam: · Marks: · Difficulty:

If $x+y+z=0$, then $x^{2}+x y+y^{2}$ equals

(a)$y^{2}+y z+z^{2}$

(b)$y^{2}-y z+z^{2}$

(c)$z^{2}-z x+x^{2}$

(d)$z^{2}+z x+x^{2}$

Answer

Answer (as printed): D

Explanation

$x+y+z=0 \Rightarrow y=-(x+z)$. $$\begin{aligned} \therefore \quad x^{2}+x y+y^{2} & =x^{2}+x(-x-z)+(x+z)^{2} \\ & =x^{2}-x^{2}-x z+x^{2}+z^{2}+2 x z \\ & =x^{2}+z^{2}+z x . \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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