Question : If $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=3$, then what is the value of $(x+y+z)^3$?
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 3
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Correct Answer: 0
Solution :
Given:$\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=3$
We know the identity, if $(x+y+z)=0$, then $(x^3+y^3+z^3)=3xyz$
Take the LCM of the given expression, we get–
$\frac{x^3+y^3+z^3}{xyz}=3$
${x^3+y^3+z^3}=3(xyz)$
So, $(x+y+z)=0$
The value of $(x+y+z)^3=0$
Hence, the correct answer is 0.
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