tìm GTNN : B= x ² + y ² + 4x +6x +15 Tìm GTLN: -x ² + 2x – 3

Question

tìm GTNN :
B= x ² + y ² + 4x +6x +15
Tìm GTLN:
-x ² + 2x – 3

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Hưng Khoa 1 year 2020-10-21T00:23:23+00:00 1 Answers 67 views 0

Answers ( )

    0
    2020-10-21T00:24:52+00:00

    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 $x=1$

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )