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Lê Anh Duy

01/09/2018 at 16:02
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28) Given x2 + 5y2 - 4xy - x + 2y - 6 = 0

Find the max and min values of A = x - 2y


MaximumMinimummemorable equality


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    Alone 23/10/2018 at 13:01

    \(x^2+5y^2-4xy-x+2y-6=0\)

    \(\Leftrightarrow x^2-4xy+4y^2-\left(x-2y\right)-6=-y^2\)

    \(\Leftrightarrow\left(x-2y\right)^2-\left(x-2y\right)-6=-y^2\le0\)

    \(\Leftrightarrow\left(x-2y+2\right)\left(x-2y-3\right)\le0\)

    \(\Leftrightarrow-2\le x-2y\le3\)

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