Đáp án:
$\min S = \dfrac{9}{5} \Leftrightarrow (x;y) = \left(\dfrac35;\dfrac65\right)$
Giải thích các bước giải:
$\begin{array}{l}\text{Ta có:}\\ x + 2y = 3\\ \to x = 3 - 2y\\ \text{Ta được:}\\ S= x^2 + y^2\\ \to S = (3 - 2y)^2 + y^2\\ \to S = 9 - 12y + 4y^2 + y^2\\ \to S = 5y^2 - 12y + 9\\ \to S = 5\left(y^2 - 2.\dfrac{6}{5}y + \dfrac{36}{25}\right) + \dfrac{9}{5}\\ \to S = 5\left(y - \dfrac65\right)^2 + \dfrac{9}{5}\\ \to S \geq 5.0 + \dfrac{9}{5}\\ \to S \geq \dfrac{9}{5}\\ \text{Dấu = xảy ra} \,\,\Leftrightarrow y = \dfrac65 \to x = \dfrac35\\ Vậy\,\,\min S = \dfrac{9}{5} \Leftrightarrow (x;y) = \left(\dfrac35;\dfrac65\right)\end{array}$
