Question

[toàn mc47]

Dạng tìm GTNN-GTLN
vd:x^2+2x+3=x^2+2x.1+1+2=x+1)^2+2 

Answer 1

[Gia Huy]

1

\(A=x^2-8x+1=x^2-2.4x+16-15\\ =\left(x-4\right)^2-15\ge-15\)

Min A \(=-15\) khi \(x=4\)

2

\(B=x^2-3x+2=x^2-2.\dfrac{3}{2}+\dfrac{9}{4}-\dfrac{1}{4}\\ =\left(x-\dfrac{3}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)

Min B \(=-\dfrac{1}{4}\) khi \(x=\dfrac{3}{2}\)

3

\(C=x^2+12x=x^2+2.6x+6^2-36\\=\left(x+6\right)^2-36\ge-36\)

Min C \(=-36\) khi `x=-6`

4

\(D=9x^2+12x-4\\ =\left(3x\right)^2+2.3x.2+2^2-8\\ =\left(3x-2\right)^2-8\ge-8\)

Min D \(=-8\) khi \(x=\dfrac{2}{3}\)

5

\(E=36x^2-60x+7=\left(6x\right)^2-2.6x.5+5^2-18\\ =\left(6x-5\right)^2-18\ge-18\)

Min E \(=-18\) khi \(x=\dfrac{5}{6}\)

Answer 2

[Nguyễn Lê Phước Thịnh]

6:

=y^2+y+1/4-1/4

=(y+1/2)^2-1/4>=-1/4

Dấu = xảy ra khi y=-1/2

7:

=5(x^2+4/5x-3/5)

=5(x^2+2*x*2/5+4/25-19/25)

=5(x+2/5)^2-19/5>=-19/5

Dấu = xảy ra khi x=-2/5

8: =7(x^2-12/7x-6/7)

=7(x^2-2*x*6/7+36/49-78/49)

=7*(x-6/7)^2-78/7>=-78/7

Dấu = xảy ra khi x=6/7

9: =x^2-2x+1+y^2-4y+4

=(x-1)^2+(y-2)^2>=0

Dấu = xảy ra khi x=1 và y=2

10: =x^2-x+1/4+1/4

=(x-1/2)^2+1/4>=1/4

Dấu = xảy ra khi x=1/2