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, 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.
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.
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