tìm GTNN : A= 2x^2+10x-1

$2x^2+10x-1$

$=(\sqrt{2}x)^2+2.\sqrt{2}x.\dfrac{5\sqrt{2}}{2}+\dfrac{25}{2}-\dfrac{27}{2}$

$=\Big(\sqrt{2}x+\dfrac{5\sqrt{2}}{2}\Big)^2-\dfrac{27}{2}$

Ta thấy: $\Big(\sqrt{2}x+\dfrac{5\sqrt{2}}{2}\Big)^2≥0$

$→\Big(\sqrt{2}x+\dfrac{5\sqrt{2}}{2}\Big)^2-\dfrac{27}{2}≥-\dfrac{27}{2}$

$→$ Dấu "=" xảy ra khi $\sqrt{2}x+\dfrac{5\sqrt{2}}{2}=0$

$→\sqrt{2}x=-\dfrac{5\sqrt{2}}{2}$

$→x=-\dfrac{5\sqrt{2}}{4}$

$→A_{min}=-\dfrac{27}{2}$