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Equation has two solutions and the sum of them equals 12

Source: Czech and Slovak MO, 2002, P4

September 15, 2012
algebrafunctiondomaingeometrygeometric transformationalgebra unsolved

Problem Statement

Find all pairs of real numbers a,ba, b for which the equation in the domain of the real numbers ax2−24x+bx2−1=x\frac{ax^2-24x+b}{x^2-1}=x has two solutions and the sum of them equals 1212.
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