MathDB
x,y,z form a geometric progression

Source: 1978 AHSME Problem 24

June 18, 2014
ratiogeometric sequenceAMC

Problem Statement

If the distinct non-zero numbers x(yz), y(zx), z(xy)x ( y - z),~ y(z - x),~ z(x - y ) form a geometric progression with common ratio rr, then rr satisfies the equation
<spanclass=latexbold>(A)</span>r2+r+1=0<spanclass=latexbold>(B)</span>r2r+1=0<spanclass=latexbold>(C)</span>r4+r21=0<span class='latex-bold'>(A) </span>r^2+r+1=0\qquad<span class='latex-bold'>(B) </span>r^2-r+1=0\qquad<span class='latex-bold'>(C) </span>r^4+r^2-1=0
<spanclass=latexbold>(D)</span>(r+1)4+r=0<spanclass=latexbold>(E)</span>(r1)4+r=0\qquad<span class='latex-bold'>(D) </span>(r+1)^4+r=0\qquad <span class='latex-bold'>(E) </span>(r-1)^4+r=0