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prove that 5n-(2n+3)(2+1) is always negative

 Jan 22, 2019
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\(5n-(2n+3)(2n+1) \text{ (what I assume you meant)} =\\ 5n - 4n^2-8n-3 =\\ -n^2 - 13n -3 = \\ -\left(n^2+13n + \dfrac{13}{2}\right)-\dfrac{13}{2}-3 = \\ -\left(n+\dfrac{13}{2}\right)^2 - \dfrac{19}{2}\\ \text{and this is clearly negative}\)

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 Jan 22, 2019

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