\(C=16x^2-8x+2024\)

\(\Rightarrow C=16x^2-8x+1+2023\)

\(\Rightarrow C=\left(4x-1\right)^2+2023\ge2023\left(\left(4x-1\right)^2\ge0\right)\)

\(\Rightarrow Min\left(C\right)=2023\)

\(D=-25x^2+50x-2023\)

\(\Rightarrow D=-\left(25x^2-50x+25\right)-1998\)

\(\Rightarrow D=-\left(5x-5\right)^2-1998\le1998\left(-\left(5x-5\right)^2\le0\right)\)

\(\Rightarrow Max\left(D\right)=1998\)

\(B=-x^2+20x+100=-\left(x^2-20x+100\right)+200=-\left(x-10\right)^2+200\le200\left(-\left(x-10\right)^2\le0\right)\)

\(\Rightarrow Max\left(B\right)=200\)

\(E=\left(2x-1\right)^2-\left(3x+2\right)\left(x-5\right)\)

\(\Rightarrow E=4x^2-4x+1-\left(3x^2-13x-10\right)\)

\(\Rightarrow E=4x^2-4x+1-3x^2+13x+10\)

\(\Rightarrow E=x^2+9x+11=x^2+9x+\dfrac{81}{4}-\dfrac{81}{4}+11\)

\(\Rightarrow E=\left(x+\dfrac{9}{2}\right)^2-\dfrac{37}{4}\ge-\dfrac{37}{4}\left(\left(x+\dfrac{9}{2}\right)^2\ge0\right)\)

\(\Rightarrow Min\left(E\right)=-\dfrac{37}{4}\)

\(F=\left(3x-5\right)^2-\left(3x+2\right)\left(4x-1\right)\)

\(\Rightarrow F=9x^2-30x+25-\left(12x^2+3x-2\right)\)

\(\Rightarrow F=-3x^2-33x+27=-3\left(x^2-10x+9\right)\)

\(\Rightarrow F=-3\left(x^2-10x+25\right)+48=-3\left(x-5\right)^2+48\le48\left(-3\left(x-5\right)^2\le0\right)\)

\(\Rightarrow Max\left(F\right)=48\)

`a)16x^2-24x+9=25`

`<=>(4x-3)^2=25`

`+)4x-3=5`

`<=>4x=8<=>x=2`

`+)4x-3=-5`

`<=>4x=-2`

`<=>x=-1/2`

`b)x^2+10x+9=0`

`<=>x^2+x+9x+9=0`

`<=>x(x+1)+9(x+1)=0`

`<=>(x+1)(x+9)=0`

`<=>` \(\left[ \begin{array}{l}x=-9\\x=-1\end{array} \right.\) 

`c)x^2-4x-12=0`

`<=>x^2+2x-6x-12=0`

`<=>x(x+2)-6(x+2)=0`

`<=>(x+2)(x-6)=0`

`<=>` \(\left[ \begin{array}{l}x=-2\\x=6\end{array} \right.\) 

`d)x^2-5x-6=0`

`<=>x^2+x-6x-6=0`

`<=>x(x+1)-6(x+1)=0`

`<=>(x+1)(x-6)=0`

`<=>` \(\left[ \begin{array}{l}x=6\\x=-1\end{array} \right.\) 

`e)4x^2-3x-1=0`

`<=>4x^2-4x+x-1=0`

`<=>4x(x-1)+(x-1)=0`

`<=>` \(\left[ \begin{array}{l}x=1\\x=-\dfrac14\end{array} \right.\) 

`f)x^4+4x^2-5=0`

`<=>x^4-x^2+5x^2-5=0`

`<=>x^2(x^2-1)+5(x^2-1)=0`

`<=>(x^2-1)(x^2+5)=0`

Vì `x^2+5>=5>0`

`=>x^2-1=0<=>x^2=1`

`<=>` \(\left[ \begin{array}{l}x=1\\x=-1\end{array} \right.\) 

\(a,=\left(5x-1\right)^2\\ b,=\left(x+4\right)^2\\ c,=\left(4x+3y\right)^2\\ d,=\left(\dfrac{x}{4}+2y\right)^2\)

Phương trình 16x² − 24x + 9 = 0

có a = 16; b’ = −12; c = 9 suy ra

Δ ' = b ' 2 − a c = (−12)² – 9.16 = 0

Nên phương trình có nghiệm kép

Đáp án cần chọn là: C

Ta có

B   =   4   –   16 x 2   –   8 x     =   5   –   ( 16 x 2   +   8 x   +   1 )   =   5   –   [ ( 4 x ) 2   +   2 . 4 x . 1   +   1 2 ]     =   5   –   ( 4 x   +   1 ) 2

Nhận thấy 4 x   +   1 2 ≥ 0; Ɐx

=> 5 – 4 x   +   1 2 ≤ 5

Dấu “=” xảy ra khi 4 x   +   1 2 = 0 ó x = - 1 4

Đáp án cần chọn là: A

`A=16x^2+8x+5`

`=16x^2+8x+1+4`

`=(4x+1)^2+4>=4`

Dấu "=" xảy ra khi `4x+1=0<=>x=-1/4`

`B=x^2-x`

`=x^2-x+1/4-1/4`

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

Dấu "=" xảy ra khi `x=1/2`

`C=a^2-2a+b^2+6b+2021`

`=a^2-2a+1+b^2+6b+9+2011`

`=(a-1)^2+(b+3)^2+2011>=2011`

Dấu "=" xảy ra khi \(\begin{cases}a=1\\b=-3\\\end{cases}\)

16x² - 2xy² - 3y² + 24x = -336

\(\Leftrightarrow\) 16x² - 2xy² - 3y² + 24x = -336

\(\Leftrightarrow\) 2x(8x - y²) + 3(8x - y²) = -336

\(\Leftrightarrow\) (8x - y²)(2x + 3) = -336

Đến đây chắc tự tìm được r

Chúc bn học tốt!

\(A\ge1\forall x\)

Dấu '=' xảy ra khi x=12

\(A=x^2-24x+144+1=\left(x-12\right)^2+1\ge1\\ A_{min}=1\Leftrightarrow x=12\)