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(x-3)/(x-6)^2 -(x-6)/{(x-3)^2=a(b-9x+x^2) (I Soros Olympiad 1994-95 R2 10.4)

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May 25, 2024
algebra

Problem Statement

It is known that for some aa and bb the equation x−3(x−6)2−x−6(x−3)2=a(b−9x+x2)\frac{x-3}{(x-6)^2} -\frac{x-6}{(x-3)^2} =a(b-9x+x^2) has as its largest root the number 19951995. Find the smallest root of this equation for the same aa and bb.
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