Toán tìm GTNN : B= x ² + y ² + 4x +6x +15 Tìm GTLN: -x ² + 2x – 3 07/07/2021 By Hadley tìm GTNN : B= x ² + y ² + 4x +6x +15 Tìm GTLN: -x ² + 2x – 3
a) $x^2+y^2+4x+6x+15$ $=x^2+y^2+10x+15$ $=x^2+y^2+10x+25-10$ $=(x^2+10x+25)+y^2-10$ $=(x+5)^2+y^2-10$ Ta thấy: $(x+5)^2≥0;y^2≥0$ $→$ Dấu “=” xảy ra khi $x+5=0;y=0$ $→x=-5;y=0$ $→B_{min}=-10$ khi $x=-5;y=0$ b) Đặt $-x^2+2x-3=A$ $=-(x^2-2x+3)$ $=-(x^2-2x+1+2)$ $=-(x^2-2x+1)-2$ $=-(x-1)^2-2$ Ta thấy: $-(x-1)^2≤0$ $→$ Dấu “=” xảy ra khi $x-1=0$ $→x=1$ $→A_{max}=-2$ khi $x=1$ Trả lời