Question of The Day30-12-2019

If x+y+z=0, then \(\frac{x^2 + yz}{yz}+\frac{y^2 + zx}{zx}+\frac{z^2 + xy}{xy}=?\)


Correct Answer : b ) 6

Explanation :

Consider the given expression

\(\frac{x^2 +yz}{yz}+\frac{y^2 + zx}{zx}+\frac{z^2 + xy}{xy}\)




As x+y+z=0

So, x3+y3+z3= 3xyz

Thus, putting the value of (x3+y3+z3) in our expression we get

\(\Rightarrow \frac{x^3+y^3+z^3+3xyz}{xyz}\)

\(\Rightarrow \frac{3xyz+3xyz}{xyz}\)

= 6

Hence, (b) is the correct answer.

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