a)\(A=5-8x-2x^2\)

\(=-2\left(x^2+4x-\frac{5}{2}\right)\)

\(=-2\left(x^2+4x+4-\frac{13}{2}\right)\)

\(=-2\left[\left(x+2\right)^2-\frac{13}{2}\right]\)

\(=-2\left[\left(x+2\right)^2\right]+13\le13\)

Vậy \(A_{max}=13\Leftrightarrow x+2=0\Leftrightarrow x=-2\)

a,A=(2x)²-2.2x.2+2²+11=(2x-2)²+11

Vì (2x-2)²luôn lớn hơn hoặc bằng 0

=>A>hoặc =0+11 hay a>hoặc =11

vậy GTNN của A là 11 khi x=1

P=(-x^2+8x-7)/(2x+2)

P-1=-(x^2-8x+7+x^2+1)/2(x+1)

P-1=-(2x^2-8x+8)/2(x+1)

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

P-1=-2(x-2)^2/2(x+1)

Vì -2(x-2)^2/2(x+1) ≥0

=> P-1≥0

=>P≥1

Dấu = xảy ra khi x-2=0 =>x=2

Vậy Pmin = 3 khi x = 2

2:

a: =-(x^2-12x-20)

=-(x^2-12x+36-56)

=-(x-6)^2+56<=56

Dấu = xảy ra khi x=6

b: =-(x^2+6x-7)

=-(x^2+6x+9-16)

=-(x+3)^2+16<=16

Dấu = xảy ra khi x=-3

c: =-(x^2-x-1)

=-(x^2-x+1/4-5/4)

=-(x-1/2)^2+5/4<=5/4

Dấu = xảy ra khi x=1/2

1) 

a) \(A=x^2+4x+17\)

\(A=x^2+4x+4+13\)

\(A=\left(x+2\right)^2+13\) 

Mà: \(\left(x+2\right)^2\ge0\) nên \(A=\left(x+2\right)^2+13\ge13\)

Dấu "=" xảy ra: \(\left(x+2\right)^2+13=13\Leftrightarrow x=-2\)

Vậy: \(A_{min}=13\) khi \(x=-2\)

b) \(B=x^2-8x+100\)

\(B=x^2-8x+16+84\)

\(B=\left(x-4\right)^2+84\)

Mà: \(\left(x-4\right)^2\ge0\) nên: \(A=\left(x-4\right)^2+84\ge84\)

Dấu "=" xảy ra: \(\left(x-4\right)^2+84=84\Leftrightarrow x=4\)

Vậy: \(B_{min}=84\) khi \(x=4\)

c) \(C=x^2+x+5\)

\(C=x^2+x+\dfrac{1}{4}+\dfrac{19}{4}\)

\(C=\left(x+\dfrac{1}{2}\right)^2+\dfrac{19}{4}\)

Mà: \(\left(x+\dfrac{1}{2}\right)^2\ge0\) nên \(A=\left(x+\dfrac{1}{2}\right)^2+\dfrac{19}{4}\ge\dfrac{19}{4}\)

Dấu "=" xảy ra: \(\left(x+\dfrac{1}{2}\right)^2+\dfrac{19}{4}=\dfrac{19}{4}\Leftrightarrow x=-\dfrac{1}{2}\)

Vậy: \(A_{min}=\dfrac{19}{4}\) khi \(x=-\dfrac{1}{2}\)

1:

a: A=x^2+4x+4+13

=(x+2)^2+13>=13

Dấu = xảy ra khi x=-2

b; =x^2-8x+16+84

=(x-4)^2+84>=84

Dấu = xảy ra khi x=4

c: =x^2+x+1/4+19/4

=(x+1/2)^2+19/4>=19/4

Dấu = xảy ra khi x=-1/2

Max A = -7

sory lộn 

TT

\(A=-2x^2+8x-15\)

\(-A=2x^2-8x+15\)

\(-A=2\left(x^2-4x+4\right)+7\)

\(-A=2\left(x-2\right)^2+7\)

Mà  \(\left(x-2\right)^2\ge0\forall x\Rightarrow2\left(x-2\right)^2\ge0\forall x\)

\(\Rightarrow-A\ge7\)

\(\Leftrightarrow A\le-7\)

Dấu "=" xảy ra khi : 

\(x-2=0\Leftrightarrow x=2\)

Vậy  \(A_{Max}=7\Leftrightarrow x=2\)

\(B=-5x\left(x+2\right)\)

\(B=-5x^2-10x\)

\(-B=5x^2+10x\)

\(-B=5\left(x^2+2x+1\right)-5\)

\(-B=5\left(x+1\right)^2-5\)

Mà  \(\left(x+1\right)^2\ge0\forall x\Leftrightarrow5\left(x+1\right)^2\ge0\forall x\)

\(\Rightarrow-B\ge-5\)

\(\Leftrightarrow B\le5\)

Dấu "=" xảy ra khi : 

\(x+1=0\Leftrightarrow x=-1\)

Vậy  \(B_{Max}=5\Leftrightarrow x=-1\)

M = -x² - 8x + 5 

= -( x² + 8x + 16 ) + 21

= -( x + 4 )² + 21 ≤ 21 ∀ x

Dấu "=" xảy ra <=> x = -4

Vậy MaxM = 21

\(M=-x^2-8x\)\(+5\)

\(=-x^2-8x-16+21\)

\(=-\left(x^2+8x+16\right)+21\)

\(=-\left(x+4\right)^2+21\)

Vì \(\left(x+4\right)^2\ge0\)

\(\Rightarrow-\left(x+4\right)^2\le0\)

\(\Rightarrow M=-\left(x+4\right)^2+21\le21\)

Dấu " = " xảy ra \(\Leftrightarrow\) \(\left(x+4\right)^2=0\)

\(\Leftrightarrow x+4=0\)

\(\Leftrightarrow x=-4\)

Vậy GTLN của M = 21 khi x = - 4