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

## Answer

Correct Answer : b ) 6

Explanation :Consider the given expression

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

or

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

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

As x+y+z=0

So, x^{3}+y^{3}+z^{3}= 3xyz

Thus, putting the value of (x^{3}+y^{3}+z^{3}) 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.

Questions related to Algebra are asked in exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, etc.

Read Daily Current Affairs, Daily Banking Affairs, Word of the Day, and much more at PendulumEdu to prepare well for the actual exam.