Toán Lớp 8: Tìm GTNN của A= 3x^2+4y^2+4xy+2x-4y+26
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Toán Lớp 8: Tìm GTNN của A= 3x^2+4y^2+4xy+2x-4y+26
Comments ( 1 )
A= 3x²+ 4y+ 4xy²+2x – 4y+26
= 4y² + (4xy – 4y) + [(x – 1)² – (x – 1)²] + 3x² + 2x + 26
= [(2y²) + 4y(x-1) + (x-1)²] – (x² – 2x + 1) + 3x² + 2x + 26
= (2y + x-1)² + 2x² + 4x + 25
= (2y + x-1)² + 2(x² + 2x+1) + 23
= (2y + x-1)² + 2(x+1)² + 23$\geq$ 23(x,y∈R)
text[Đồng thức xảy ra:] ⇔ \(\left[ \begin{array}{2y+x+1=0}2y+x+1=0\\x+1=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=-1\\y=1\end{array} \right.\)
Vậy $A_{min}$ =23, text[khi x=-1 y=1]
$#Zyy_mood$
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