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Algebraic expressions with a,b,c,x

Source: 1978 AHSME Problem 20

June 6, 2014
AhsmeAMCpolynomial

Problem Statement

If a,b,ca,b,c are non-zero real numbers such that a+b−cc=a−b+cb=−a+b+ca,\frac{a+b-c}{c}=\frac{a-b+c}{b}=\frac{-a+b+c}{a}, and x=(a+b)(b+c)(c+a)abc,x=\frac{(a+b)(b+c)(c+a)}{abc}, and x<0x<0, then xx equals
<spanclass=′latex−bold′>(A)</span>−1<spanclass=′latex−bold′>(B)</span>−2<spanclass=′latex−bold′>(C)</span>−4<spanclass=′latex−bold′>(D)</span>−6<spanclass=′latex−bold′>(E)</span>−8<span class='latex-bold'>(A) </span>-1\qquad<span class='latex-bold'>(B) </span>-2\qquad<span class='latex-bold'>(C) </span>-4\qquad<span class='latex-bold'>(D) </span>-6\qquad <span class='latex-bold'>(E) </span>-8
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