Algebra

Quantitative Aptitude (CDS)

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$what \;is \;\frac{(x-y)(y-z)(z-x)}{(x-y)^{3}+(y-z)^{3})+(z-x)^{3}}\;equal\;to\;?$

=-1/3

1/3

-3

Explanation:

Let, (x - y) = a, (y - z) = b and (z - x) = c
Now, a + b + c = x – y + y – z + z – x = 0
So, a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² + ab + bc + ca)
=> a³ + b³ + c³ – 3abc = 0 [As, a + b + c = 0]
Again,
a³ + b³ + c³ = 3abc
=>abc/(a³+b³+c³)=1/3
hence,
$\frac{(x-y)(y-z)(z-x)}{(x-y)^{3}+(y-z)^{3}(z-x)^{3}}=\frac{1}{3}$

By: Munesh Kumari

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