\(S=4x^2-12xy+9y^2+32x-48y+64+x^2-8x+16+2000\)
\(S=\left(2x-3y\right)^2+16\left(2x-3y\right)+64+\left(x^2+8x+16\right)+2000\)
\(S=\left(2x-3y+8\right)^{^2}+\left(x-4\right)^2+2000\ge2000\)
MinS = 2000 khi x = 4 và y = 16/3
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\(S=5x^2+9y^2-12xy+24x-48y+2028\)
\(=\left(9y^2-12xy-48y\right)+5x^2+24x+2028\)
\(=\left[\left(3y\right)^2-2.3y.\left(2x+8\right)+\left(2x+8\right)^2\right]+5x^2+24x+2028-\left(2x+8\right)^2\)\(=\left(3y-2x-8\right)^2+5x^2+24x+2028-4x^2-32x-64\)\(=\left(3y-2x-8\right)^2+\left(x^2-8x+16\right)+1948\)
\(=\left(3y-2x-8\right)^2+\left(x-4\right)^2+1948\ge1948\forall x;y\)Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}x=4\\y=\dfrac{16}{3}\end{matrix}\right.\)
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