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For specific positive numbers m and n, the quadratics 16x^2 + 44x + 56 + 4x^2 - 14x - 30 and (mx + n)^2 differ only in their constant term. What is mn?

 Jun 22, 2022
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The first quadratic simplifies to 20x^2 + 30x + 26, and the second one expands to m^2x^2 + 2mnx + n^2. As the constant terms are the only terms that are different between these two, we know that 2mnx = 30x. Simplifying, we get \(mn=\boxed{15}\)

 Jun 22, 2022

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