Không có max

`a)sqrt{x^2-2x+5}`

`=sqrt{x^2-2x+1+4}`

`=sqrt{(x-1)^2+4}`

Vì `(x-1)^2>=0`

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

`=>sqrt{(x-1)^2+4}>=sqrt4=2`

Dấu "=" xảy ra khi `x=1.`

`b)2+sqrt{x^2-4x+5}`

`=2+sqrt{x^2-4x+4+1}`

`=2+sqrt{(x-2)^2+1}`

Vì `(x-2)^2>=0`

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

`=>sqrt{(x-2)^2+1}>=1`

`=>sqrt{(x-2)^2+1}+2>=3`

Dấu "=" xảy ra khi `x=2`

Chọn A

\(C=\frac{4x^2+2x-2}{2\left(x^2-2x+2\right)}=\frac{9\left(x^2-2x+2\right)-5x^2+20x-20}{2\left(x^2-2x+2\right)}=\frac{9}{2}-\frac{5\left(x-2\right)^2}{2\left(x-1\right)^2+2}\le\frac{9}{2}\)

\(C_{max}=\frac{9}{2}\) khi \(x=2\)

\(C=\frac{4x^2+2x-2}{2\left(x^2-2x+2\right)}=\frac{-\left(x^2-2x+2\right)+5x^2}{2\left(x^2-2x+2\right)}=-\frac{1}{2}+\frac{5x^2}{2\left(x-1\right)^2+2}\ge-\frac{1}{2}\)

\(C_{min}=-\frac{1}{2}\) khi \(x=0\)

Câu D bạn coi lại đềm kết quả rất xấu: \(\frac{3-\sqrt{17}}{12}\le D\le\frac{3+\sqrt{17}}{12}\)

a)x²+2x+4+1=(x+1)²+1

ma (x+1)² >0

nen (x+1)²+1>1

vay x²+2x+5 min la 1 khi x=-1

a) \(A=\sqrt{x-2}+\sqrt{6-x}\)

\(\Rightarrow A^2=x-2+6-x+2\sqrt{\left(x-2\right)\left(6-x\right)}\)

Ta có \(\sqrt{\left(x-2\right)\left(6-x\right)}\ge0,\forall x\)

Do đó \(A^2=4+2\sqrt{\left(x-2\right)\left(6-x\right)}\ge4\)

Mà A không âm \(\Leftrightarrow A\ge2\)

Dấu "=" \(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=6\end{matrix}\right.\)

Áp dụng BĐT Bunhiacopxky:

\(A^2=\left(\sqrt{x-2}+\sqrt{6-x}\right)^2\le\left(x-2+6-x\right)\left(1+1\right)=4\cdot2=8\)

\(\Leftrightarrow A\le\sqrt{8}\)

Dấu "=" \(\Leftrightarrow x-2=6-x\Leftrightarrow x=4\)

Mấy bài còn lại y chang nha 

Tick hộ nha