Bmin=5 xay ra dau= khi va chi khi x=5

\(B=\sqrt{x^2-10x+34}+\sqrt{x^2-10x+29}\)

\(=\sqrt{\left(x-5\right)^2+9}+\sqrt{\left(x-5\right)^2+4}\)\(\ge\)\(\sqrt{9}+\sqrt{4}=5\)

Vậy Min \(B=5\)khi  \(x=5\)

a) \(\sqrt[]{x^2-4x+4}=x+3\)

\(\Leftrightarrow\sqrt[]{\left(x-2\right)^2}=x+3\)

\(\Leftrightarrow\left|x-2\right|=x+3\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=x+3\\x-2=-\left(x+3\right)\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}0x=5\left(loại\right)\\x-2=-x-3\end{matrix}\right.\)

\(\Leftrightarrow2x=-1\Leftrightarrow x=-\dfrac{1}{2}\)

b) \(2x^2-\sqrt[]{9x^2-6x+1}=5\)

\(\Leftrightarrow2x^2-\sqrt[]{\left(3x-1\right)^2}=5\)

\(\Leftrightarrow2x^2-\left|3x-1\right|=5\)

\(\Leftrightarrow\left|3x-1\right|=2x^2-5\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=2x^2-5\\3x-1=-2x^2+5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x^2-3x-4=0\left(1\right)\\2x^2+3x-6=0\left(2\right)\end{matrix}\right.\)

Giải pt (1)

\(\Delta=9+32=41>0\)

Pt \(\left(1\right)\) \(\Leftrightarrow x=\dfrac{3\pm\sqrt[]{41}}{4}\)

Giải pt (2)

\(\Delta=9+48=57>0\)

Pt \(\left(2\right)\) \(\Leftrightarrow x=\dfrac{-3\pm\sqrt[]{57}}{4}\)

Vậy nghiệm pt là \(\left[{}\begin{matrix}x=\dfrac{3\pm\sqrt[]{41}}{4}\\x=\dfrac{-3\pm\sqrt[]{57}}{4}\end{matrix}\right.\)

Bằng 0 chứ nhỉ em ?

(x-5) . (2x-4)= 0

\(\left[{}\begin{matrix}x-5=0\\2x-4=0\end{matrix}\right.< =>\left[{}\begin{matrix}x=5\\2x=4\end{matrix}\right.< =>\left[{}\begin{matrix}x=5\\x=2\end{matrix}\right.\)

a) đk: \(x\ge2\)

Ta có: \(\sqrt{x}+\sqrt{x-2}=2\sqrt{x-1}\) (đã sửa đề)

\(\Leftrightarrow x+2\sqrt{x\left(x-2\right)}=4\left(x-1\right)\)

\(\Leftrightarrow3x-4=2\sqrt{x^2-2x}\)

\(\Leftrightarrow9x^2-24x+16=4\left(x^2-2x\right)\)

\(\Leftrightarrow5x^2-16x+16=0\)

\(\Leftrightarrow5\left(x^2-\frac{16}{5}x+\frac{64}{25}\right)+\frac{16}{5}=0\)

\(\Leftrightarrow5\left(x-\frac{8}{5}\right)^2=-\frac{16}{5}\) vô lý

=> PT vô nghiệm

b) Đề chắc là: \(x^2+x+12=\sqrt{36}\)

\(\Leftrightarrow x^2+x+12-6=0\)

\(\Leftrightarrow\left(x^2+x+\frac{1}{4}\right)+\frac{23}{4}=0\)

\(\Leftrightarrow\left(x+\frac{1}{2}\right)^2=-\frac{23}{4}\) vô lý

=> PT vô nghiệm

a: \(\sqrt{x^2-4x+4}=3x+1\)

=>\(\sqrt{\left(x-2\right)^2}=3x+1\)

=>|x-2|=3x+1

=>\(\begin{cases}3x+1\ge0\\ \left(3x+1\right)^2=\left(x-2\right)^2\end{cases}\Rightarrow\begin{cases}x\ge-\frac13\\ \left(3x+1-x+2\right)\left(3x+1+x-2\right)=0\end{cases}\)

=>\(\begin{cases}x\ge-\frac13\\ \left(2x+3\right)\left(4x-1\right)=0\end{cases}\Rightarrow\begin{cases}x\ge-\frac13\\ x\in\left\lbrace-\frac32;\frac14\right\rbrace\end{cases}\)

=>\(x=\frac14\)

b:

ĐKXĐ: \(x^2-4x+1\ge0\)

=>\(x^2-4x+4-3\ge0\)

=>\(\left(x-2\right)^2\ge3\)

=>\(\left[\begin{array}{l}x-2\ge\sqrt3\\ x-2\le-\sqrt3\end{array}\right.\Rightarrow\left[\begin{array}{l}x\ge2+\sqrt3\\ x\le2-\sqrt3\end{array}\right.\)

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

=>\(\begin{cases}x\ge0\\ x^2-4x+1=x^2\end{cases}\Rightarrow\begin{cases}x\ge0\\ -4x+1=0\end{cases}\Rightarrow x=\frac14\)

c: \(\sqrt{x^2-2x+5}=x+3\)

=>\(\begin{cases}x+3\ge0\\ x^2-2x+5=\left(x+3\right)^2\end{cases}\Rightarrow\begin{cases}x\ge-3\\ x^2+6x+9=x^2-2x+5\end{cases}\)

=>\(\begin{cases}x\ge-3\\ x^2+6x+9-x^2+2x-5=0\end{cases}\Rightarrow\begin{cases}x\ge-3\\ 8x+4=0\end{cases}\Rightarrow x=-\frac12\)

d: \(\sqrt{x^2-10x+25}-2x=3\)

=>\(\sqrt{\left(x-5\right)^2}=2x+3\)

=>|x-5|=2x+3

=>\(\begin{cases}2x+3\ge0\\ \left(2x+3\right)^2=\left(x-5\right)^2\end{cases}\Rightarrow\begin{cases}x\ge-\frac32\\ \left(2x+3-x+5\right)\left(2x+3+x-5\right)=0\end{cases}\)

=>\(\begin{cases}x\ge-\frac32\\ \left(x+8\right)\left(3x-2\right)=0\end{cases}\Rightarrow x=\frac23\)

e:

ĐKXĐ: \(\left[\begin{array}{l}x\ge3\\ x\le1\end{array}\right.\)

\(\sqrt{x^2-4x+3}=x-2\)

=>\(\begin{cases}x-2\ge0\\ x^2-4x+3=\left(x-2\right)^2\end{cases}\Rightarrow\begin{cases}x\ge2\\ x^2-4x+3=x^2-4x+4\end{cases}\)

=>x∈∅

f: \(\sqrt{x^2-6x+9}=2x-1\)

=>\(\sqrt{\left(x-3\right)^2}=2x-1\)

=>|x-3|=2x-1

=>\(\begin{cases}2x-1\ge0\\ \left(2x-1\right)^2=\left(x-3\right)^2\end{cases}\Rightarrow\begin{cases}x\ge\frac12\\ \left(2x-1-x+3\right)\left(2x-1+x-3\right)=0\end{cases}\)

=>\(\begin{cases}x\ge\frac12\\ \left(x+2\right)\left(3x-4\right)=0\end{cases}\Rightarrow x=\frac43\)

Oke

Oke

\(a,ĐK:x\in R\)

\(b,ĐK:\dfrac{-7}{8-10x}\ge0\Leftrightarrow8-10x< 0\left(-7< 0\right)\Leftrightarrow x>\dfrac{4}{5}\)

\(c,ĐK:\dfrac{24-6x}{-7}\ge0\Leftrightarrow24-6x\le0\left(-7< 0\right)\Leftrightarrow x\ge4\)

a:ĐKXĐ: \(x\in R\)

b: ĐKXĐ: \(x>\dfrac{4}{5}\)

c: ĐKXĐ: x>4

GTLN ak. bạn có nhầm đề k vậy, bạn xem lại đề đi.

mình k ak

bạn giúp mình phân tích cái kia ra là đc

k tìm dc GTLN nhà bạn, bạn xem lại đề đi

Em bấm vào biểu tượng \(\sum\) trên thanh công cụ và gõ phân số để mn dễ hỗ trợ nhé!

`(x^2+x-6)/(x^2+4x+3):(x^2-10x+25)/(x^2-4x-5)(x ne -1,x ne 5,x ne -3)`

`=((x-2)(x+3))/((x+1)(x+3)):(x-5)^2/((x+1)(x-5))`

`=(x-2)/(x+1):(x-5)/(x+1)`

`=(x-2)/(x-5)`

\(\dfrac{x^2+x-6}{x^2+4x+3}=\dfrac{\left(x+3\right)\left(x-2\right)}{\left(x+3\right)\left(x+1\right)}=\dfrac{x-2}{x+1}\)

\(\dfrac{x^2-10x+25}{x^2-4x-5}=\dfrac{\left(x-5\right)^2}{\left(x-5\right)\left(x+1\right)}=\dfrac{x-5}{x+1}\)