Symbiosis National Aptitude Test SNAP 2015 Paper

Question : 21 of 150

Marks: +1, -0

If x + y + z = 0
then

x^3 + y^3 + z^3

+ 3xyz is equal to

Solution:

Given x + y + z = 0

x^3 + y^3 + z^3

+ 3xyz – 3xyz + 3xyz
=

x^3 + y^3 + z^3

–3xyz + 6xyz
= (x + y + z) (

x^2 + y^2 + z^2

– xy – yz –zx) + 6xyz
= (0) (

x^2 + y^2 + z^2

– xy – yz – zx) + 6xyz
= 6xyz

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