1. \(x+y=3\)
\(\Rightarrow B=\left(x+y\right)\left(x^2-xy+y^2\right)+9xy\)
\(B=3x^2-3xy+3y^2+9xy\)
\(B=3x^2+6xy+3y^2\)
\(B=3\left(x^2+2xy+y^2\right)\)
\(B=3\left(x+y\right)^2\)
\(B=3.3^2=27\)
2. \(Q=2x-2x^2+3=-2\left(x^2-x-\dfrac{3}{2}\right)=-2\left(x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{7}{4}\right)\)
\(Q=-2\left(x-\dfrac{1}{2}\right)^2+\dfrac{7}{2}\le\dfrac{7}{2}\)
Vậy: \(Max_Q=\dfrac{7}{2}\Leftrightarrow x=\dfrac{1}{2}\)
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