\(a,B=\frac{10\sqrt{x}+12+\sqrt{x}\left(\sqrt{x}-3\right)-\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(=\frac{x+6\sqrt{x}+9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}=\frac{\sqrt{x}+3}{\sqrt{x}-3}\)

\(b,C=\frac{x-1}{\sqrt{x}-3}:\frac{\sqrt{x}+3}{\sqrt{x}-3}=\frac{x-1}{\sqrt{x}+3}\)

Vì\(\hept{\begin{cases}x\ge0\\\sqrt{x}+3>0\end{cases}\Rightarrow}x-1\ge-1\)

\(\Rightarrow C_{min}=-1\Leftrightarrow x=0\)

Vậy................

Với x = 0 thì C = -1/3 chứ có phải là  -1 đâu .

b) 

Ta có: \(C=\frac{x-1}{\sqrt{x}+3}=\sqrt{x}-3+\frac{8}{\sqrt{x}+3}=\left(\sqrt{x}+3+\frac{9}{\sqrt{x}+3}\right)-6-\frac{1}{\sqrt{x}+3}\)

\(\ge2\sqrt{\left(\sqrt{x}+3\right).\frac{9}{\sqrt{x}+3}}-6-\frac{1}{3}=-\frac{1}{3}\)

Dấu "=" xảy ra <=> \(\hept{\begin{cases}\sqrt{x}+3=\frac{9}{\sqrt{x}+3}\\x=0\end{cases}}\Leftrightarrow x=0\)

Vậy min C = -1/3 tại  x =0

a)=15.2154/1505

=6462/301

b)=461179719/138076

c,=134724+400/135136-12

=135124/135124

=1

\(a,2\sqrt{x}+3=0\)

\(\Leftrightarrow2\sqrt{x}=-3\)

\(\Leftrightarrow\sqrt{x}=-\frac{3}{2}\)( loại )

\(b,\frac{5}{12}\sqrt{x}-\frac{1}{6}=\frac{1}{3}\Leftrightarrow\frac{5}{12}\sqrt{x}=\frac{1}{2}\Leftrightarrow\sqrt{x}=\frac{6}{5}\Leftrightarrow x=\frac{36}{25}\)

\(c,\sqrt{x+3}+3=0\Leftrightarrow\sqrt{x+3}=-3\)( loại )

Bài 1:

a) \(2\left(x-\sqrt{12}\right)^2=6\Rightarrow\left(x-\sqrt{12}\right)^2=3\)

TH1l \(x-\sqrt{12}=\sqrt{3}\Rightarrow x=\sqrt{3}+\sqrt{12}=3\sqrt{3}\)

TH2: \(x-\sqrt{12}=-\sqrt{3}\Rightarrow x=-\sqrt{3}+\sqrt{12}=\sqrt{3}\)

b)  \(2x-\sqrt{x}=0\Leftrightarrow\sqrt{x}\left(2\sqrt{x}-1\right)=0\Leftrightarrow\orbr{\begin{cases}\sqrt{x}=0\\2\sqrt{x}-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\\sqrt{x}=\frac{1}{2}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{1}{4}\end{cases}}\)

c) \(|2x+\sqrt{\frac{9}{16}}|-x=\left(\frac{1}{\sqrt{2}}\right)^2\Leftrightarrow\left|2x+\frac{3}{4}\right|-x=\frac{1}{2}\)

TH1: \(2x+\frac{3}{4}\ge0\Leftrightarrow x\ge-\frac{3}{8}\)

Ta có \(2x+\frac{3}{4}-x=\frac{1}{2}\Leftrightarrow x=-\frac{1}{4}\left(tm\right)\)

TH2: \(x< -\frac{3}{8}\)

Ta có \(-2x-\frac{3}{4}-x=\frac{1}{2}\Leftrightarrow-3x=\frac{5}{4}\Leftrightarrow x=-\frac{5}{12}\left(tm\right)\)

Bài 2:  Để \(A=\frac{2\sqrt{x}+3}{\sqrt{x}-2}\) là số nguyên thì \(\frac{2\sqrt{x}+3}{\sqrt{x}-2}\in Z\)

Ta có \(\frac{2\left(\sqrt{x}-2\right)+7}{\sqrt{x}-2}=2+\frac{7}{\sqrt{x}-2}\)

Để \(\frac{2\sqrt{x}+3}{\sqrt{x}-2}\in Z\) thì \(\frac{7}{\sqrt{x}-2}\in Z\Rightarrow\sqrt{x}-2\inƯ\left(7\right)\)

Do \(\sqrt{x}-2\ge-2\Rightarrow\sqrt{x}-2\in\left\{-1;1;7\right\}\)

\(\Rightarrow x\in\left\{1;9;81\right\}\)

 Bài 1 :

\(2\left(x-\sqrt{12}\right)^2=6\)

\(\Rightarrow\left(x-\sqrt{12}\right)^2=6:2=3\)

\(\Rightarrow x-\sqrt{12}=\sqrt{3}\)

\(\Rightarrow x=3\sqrt{3}\)

\(2x-\sqrt{x}=0\)

\(\Rightarrow2x=\sqrt{x}\)

Bài này không tồn tại x . vì :

Giả sử x = a . a  =>\(\sqrt{x}=a\)

Mà 2x = 2a^2 

=> x không tồn tại . 

\(C=\frac{2\sqrt{a}\left(\sqrt{a}-3\right)+\sqrt{a}\left(\sqrt{a}+3\right)-\left(3a+3\right)}{a-9}:\frac{2\sqrt{a}-2-\left(\sqrt{a}-3\right)}{\sqrt{a}-3}\)

\(C=\frac{2a-6\sqrt{a}+a+3\sqrt{a}-3a-3}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}.\frac{\sqrt{a}-3}{2\sqrt{a}-2-\sqrt{a}+3}\)

\(C=\frac{-3\sqrt{a}-3}{\sqrt{a}+3}.\frac{1}{\sqrt{a}+1}\)

\(C=\frac{-3}{\sqrt{a}+3}\)

Thay a = \(21-12\sqrt{3}\) vào C , ta có

\(C=\frac{-3}{\sqrt{21-12\sqrt{3}}+3}\)

\(C=\frac{-3}{\sqrt{\left(2\sqrt{3}-3\right)^2}+3}\)

\(C=\frac{-3}{2\sqrt{3}-3+3}=\frac{-3}{2\sqrt{3}}=\frac{-\sqrt{3}}{2}\)

câu C đâu ạ