Question : If $x + y + z = 6$ and $x y + y z + z x = 10$ , then the value of $x^{3} + y^{3} + z^{3} - 3 x y z$ is:
Option 1: 36
Option 2: 48
Option 3: 42
Option 4: 40

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Question : If $x y + y z + z x = 0$ , then $(\frac{1}{x^{2} - y z} + \frac{1}{y^{2} - z x} + \frac{1}{z^{2} - x y})$ $(x, y, z \neq 0)$ is equal to:

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Answer 1

Correct Answer: 36

Solution : Given: $x + y + z = 6$ and $x y + y z + z x = 10$
We know that $x^{3} + y^{3} + z^{3} - 3 x y z = (x + y + z) [(x + y + z)^{2} - 3 (x y + y z + z x)]$
Substituting the given values, we get
$x^{3} + y^{3} + z^{3} - 3 x y z$
$= 6 [6^{2} - 3 (10)] = 6 (36 - 30)$
$= 6 \times 6 = 36$
Hence, the correct answer is 36.

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Question : If x+y+z=6 and xy+yz+zx=10, then the value of x3+y3+z3−3xyz is:Option 1: 36Option 2: 48Option 3: 42Option 4: 40

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Question : If $x + y + z = 6$ and $x y + y z + z x = 10$ , then the value of $x^{3} + y^{3} + z^{3} - 3 x y z$ is:
Option 1: 36
Option 2: 48
Option 3: 42
Option 4: 40