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Simultaneous quadratic equations

Source: SAMO 2016 Q2

September 24, 2016
quadratic equationalgebra

Problem Statement

Determine all pairs of real numbers aa and bb, b>0b > 0, such that the solutions to the two equations x2+ax+a=bandx2+ax+a=āˆ’bx^2 + ax + a = b \qquad \text{and} \qquad x^2 + ax + a = -b are four consecutive integers.
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