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[Tu Annh]

Tim GTLNcua B=1-{x}^2+3x
Chox+2y=1 .Tim GTNN cua {x}^2+2{y}^2.Xin giai chi tiet

[Lanyes]

Tim GTLNcua B=1-{x}^2+3x
Chox+2y=1 .Tim GTNN cua {x}^2+2{y}^2.Xin giai chi tiet

1/$1 - x^2 + 3x = - (x^2 - 3x + \dfrac{9}{4}) + \dfrac{{13}}{4} \le \dfrac{{13}}{4} $
2/ Theo BĐT Cauchy-Schwarz $\begin{array}{l}

(x + 2y)^2 = (1.x + \sqrt 2 .\sqrt 2 .y)^2 \le (1 + 2)(x^2 + 2y^2 ) \\
\Rightarrow x^2 + 2y^2 \ge \dfrac{1}{3} \\
\end{array} $