MathDB
Turkey NMO 2000 1st Round - P24 (Algebra)

Source:

July 25, 2012

Problem Statement

Let a,b,c,d,ea,b,c,d,e be non-negative real numbers such that a+b+c+d+e>0a+b+c+d+e>0. What is the least real number tt such that a+c=tba+c=tb, b+d=tcb+d=tc, c+e=tdc+e=td?
<spanclass=latexbold>(A)</span> 22<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 32<spanclass=latexbold>(E)</span> 2 <span class='latex-bold'>(A)</span>\ \frac{\sqrt 2}2 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ \sqrt 2 \qquad<span class='latex-bold'>(D)</span>\ \frac32 \qquad<span class='latex-bold'>(E)</span>\ 2