If x2 yz y2 zx z2 xy 3 then what is the value of x y z 3 ........

Quantitative Aptitude (CGL) Algebra

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If (x²/yz) + (y²/zx) + (z²/xy) = 3, then what is the value of (x + y + z)³?

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Explanation:

If (x²/yz) + (y²/zx) + (z²/xy) = 3
=> x³/xyz + y³/xyz + z³/xyz = 3
=> (x³ + y³ + z³)/xyz = 3
=> x³ + y³ + z³ = 3xyz
we know, when a + b + c = 0
then , a³ + b³ + c³ = 3abc
here, x³ + y³ + z³ = 3xyz
then, x + y + z = 0
so, (x + y + z)³ = (0)³ = 0
hence, (x + y + z)³ = 0