Question

Answer 1

\(A=3\left(x^2+\dfrac{4}{3}x\right)+\left(y^2-y+\dfrac{1}{4}\right)-\dfrac{1}{4}\\ A=3\left(x^2+2\cdot\dfrac{2}{3}x+\dfrac{4}{9}\right)+\left(y-\dfrac{1}{2}\right)^2-\dfrac{19}{12}\\ A=3\left(x+\dfrac{2}{3}\right)^2+\left(y-\dfrac{1}{2}\right)^2-\dfrac{19}{12}\ge-\dfrac{19}{12}\\ A_{min}=-\dfrac{19}{12}\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{2}{3}\\y=\dfrac{1}{2}\end{matrix}\right.\)