Giải thích các bước giải:
Ta có :
$5x+2y=10\to y=\dfrac{10-5x}{2}$
$\to A=3x.\dfrac{10-5x}{2}-x^2-(\dfrac{10-5x}{2})^2$
$\to A=\dfrac{-59x^2+160x-100}{4}$
$\to A=-\dfrac{59x^2-160x+100}{4}$
$\to A=-\dfrac{59\left(x-\dfrac{80}{59}\right)^2-\dfrac{500}{59}}{4}$
$\to A=-\dfrac{59\left(x-\dfrac{80}{59}\right)^2}{4}+\dfrac{500}{236}$
Vì $\dfrac{59\left(x-\dfrac{80}{59}\right)^2}{4}\ge 0\quad\forall x$
$\to -\dfrac{59\left(x-\dfrac{80}{59}\right)^2}{4}\le 0$
$\to -\dfrac{59\left(x-\dfrac{80}{59}\right)^2}{4}+\dfrac{500}{236}\le\dfrac{500}{236} $
$\to A\le \dfrac{500}{236}$
$\to GTLN_A=\dfrac{500}{236}$
Khi đó $x=\dfrac{80}{59}\to y=\dfrac{95}{59}$
