Giải thích các bước giải:
Ví dụ 37:
Ta có :
$S=(a^2-2a+1)+(b^2+2b+1)+5=(a-1)^2+(b+1)^2+5\ge (a-1)^2+(b+1)^2+5\ge 5$
$\to Min S=5\to a=1,b=-1$
Ví dụ 38:
$T=x-2\sqrt{x}(\sqrt{y}+1)+(\sqrt{y}+1)^2+2y-2\sqrt{y}+4$
$\to T=(\sqrt{x}-(\sqrt{y}+1))^2+2(\sqrt{y}-\dfrac{1}{4})^2+\dfrac{7}{2}\ge \dfrac{7}{2}$
$\to Min T=\dfrac{7}{2}\to y=\dfrac{1}{6}, x=\dfrac{25}{16}$