$-x^2+10x-2$
$=-(x^2-10x+2)$
$=-(x^2-2.5.x+5^2-23)$
$=-(x-5)^2+23$
$(x-5)^2≥0$
$⇒-(x-5)^2≤0$
$-(x-5)^2+23≤23$
Vậy $-x^2+10x-2$ đạt GTLN là $23$ khi $x=5$
$-2x^2+2x+3$
$=-2(x^2-x-\dfrac{3}{2})$
$=-2(x-\dfrac{1}{2})^2+\dfrac{7}{2}$
Mà $(x-\dfrac{1}{2})^2≥0$
$⇒-2(x-\dfrac{1}{2})^2≤0$
$-2(x-\dfrac{1}{2})^2+\dfrac{7}{2}≤\dfrac{7}{2}$
Vậy $-2x^2+2x+3$ đạt GTLN là $\dfrac{7}{2}$ khi $x=\dfrac{1}{2}$
