Question : If $\small x+y+z=6$ and $xy+yz+zx=10$, then the value of $x^{3}+y^{3}+z^{3}-3xyz$ is:
Option 1: 36
Option 2: 48
Option 3: 42
Option 4: 40
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Correct Answer: 36
Solution :
Given: $x+y+z=6$ and $xy+yz+zx=10$
We know that $x^{3}+y^{3}+z^{3}-3xyz=(x + y + z) [(x + y + z)^2 - 3 (x y + y z + z x)]$
Substituting the given values, we get
$x^{3}+y^{3}+z^{3}-3xyz$
$=6[6^2-3(10)]=6(36-30)$
$=6\times6=36$
Hence, the correct answer is 36.
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