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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Main · Mathematics · Basics of Mathematics

If a=(x)/(y-z), b=(y)/(z-x) and c=(z)/(x-y) , where x, y and z are...

If a=xy−z,b=yz−xa=\frac{x}{y-z}, b=\frac{y}{z-x} and c=zx−yc=\frac{z}{x-y}, where x,yx, y and zz are not all zero, then what is the value of ab+bc+ca=a b+b c+c a= ?

Options

  1. A0
  2. B-1
  3. C+1
  4. D2

Correct answer

B. -1

Step-by-step solution

We have, a=xy−z,\frac{x}{y-z},b=yz−x,\frac{y}{z-x},c=zx−y\frac{z}{x-y}where, x,y,z≠0x, y, z \neq 0 Put x=1, y=2  and \text { and }z=3 a=12−3=−1b=23−1=1c=31−2=−3\begin{aligned}& a=\frac{1}{2-3}=-1 \\ & b=\frac{2}{3-1}=1 \\ & c=\frac{3}{1-2}=-3 \end{aligned}Now, ab+bc+ca=−1−3+3=−1a b+b c+c a=-1-3+3=-1 \therefore a b+b c+c a=-1
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