JEE Main 2014 · 9 Apr · Shift 1 · Mathematics Q65

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MathematicsSingle correct+4 / -1Question 65 of 90

If $a$ , $b$ , $c$ are non - zero real numbers and if the system of equations
$(a-1)x=y+z,\qquad(b-1)y=z+x,\qquad(c-1)z=x+y,$
has a non-trivial solution, then $ab+bc+ca$ equals :

a+b+c

abc

-1

Answer and worked solution

Official answer: B

Add $x$ , $y$ , $z$ to each equation: $ax=by=cz=s$ , where $s=x+y+z$ . For a non-trivial solution $s\ne0$ , and then
$s=\frac sa+\frac sb+\frac sc\implies\frac1a+\frac1b+\frac1c=1\implies ab+bc+ca=abc.$

Topics:Systems of linear equations

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JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 65