$\left \{ {{2x+3y+1=0} \atop {2y-1/2=0}} \right.$ 4x2+13y2+4x+4y−12xy+20
=[(2x)²+(3y)²+1²+2.2x.1+2.3y.1+2.2x.3y]+[(2y)²-2.2y.$\frac{1}{2}$+$\frac{1}{4}$]+18,75
=(2x+3y+1)²+(2y-$\frac{1}{2}$)²+18,75
Có (2x+3y+1)²≥0
(2y-$\frac{1}{2}$)²≥0
⇒(2x+3y+1)²+(2y-$\frac{1}{2}$)²≥0
⇒(2x+3y+1)²+(2y-$\frac{1}{2}$)²+18,75≥18,75
Dấu ''='' sảy ra ⇔ \(\left[ \begin{array}{l}2x+3y+1=0\\2y-1/2=0\end{array} \right.\)
⇔$\left \{ {{2x+3y=-1} \atop {y=1/4}} \right.$
⇔$\left \{ {{y=1/4} \atop {x=-7/8}} \right.$
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