Toán Lớp 8: x^2+y^2 – xy – x + y + 1 tìm GTNN
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Toán Lớp 8: x^2+y^2 – xy – x + y + 1 tìm GTNN
1 câu thôi ạ!!!!! giúp em vs em đang cần gấp
Comments ( 1 )
=(x²-xy+$\frac{y²}{4}$)-($\frac{x-y}{2}$)+$\frac{1}{4}$+$\frac{3}{4}$(y²+$\frac{2y}{3}$+$\frac{1}{9}$)+$\frac{2}{3}$
=($\frac{x-y}{2}$-$\frac{1}{2}$)²+$\frac{3}{4}$(y+$\frac{1}{3}$)²+$\frac{2}{3}$
Ta có: ($\frac{x-y}{2}$-$\frac{1}{2}$ )²≥ 0; $\frac{3}{4}$ (y+$\frac{1}{3}$ )²≥ 0
=>($\frac{x-y}{2}$ -$\frac{1}{2}$ )²+$\frac{3}{4}$ (y+$\frac{1}{3}$ )²+$\frac{2}{3}$ ≥ $\frac{2}{3}$
=>MinA=$\frac{2}{3}$ <=>y=$\frac{-1}{3}$ , x=$\frac{1}{3}$