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Moldova mo 2006, 10th grade

Source: Moldova MO 2006

March 21, 2006
parameterizationlogarithmsalgebra unsolvedalgebra

Problem Statement

Find all real values of the real parameter aa such that the equation 2x2−6ax+4a2−2a−2+log⁡2(2x2+2x−6ax+4a2)= 2x^{2}-6ax+4a^{2}-2a-2+\log_{2}(2x^{2}+2x-6ax+4a^{2})= =log⁡2(x2+2x−3ax+2a2+a+1). =\log_{2}(x^{2}+2x-3ax+2a^{2}+a+1). has a unique solution.
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