ĐKXĐ: \(x\ge\frac{2}{3}\)
\(\Leftrightarrow\sqrt{4x+1}-3+\sqrt{3x-2}-2=0\)
\(\Leftrightarrow\frac{4x-8}{\sqrt{4x+1}+3}+\frac{3x-6}{\sqrt{3x-2}+2}=0\)
\(\Leftrightarrow\left(x-2\right)\left(\frac{2}{\sqrt{4x+1}+3}+\frac{2}{\sqrt{3x-2}+2}\right)=0\)
\(\Leftrightarrow x=2\)
Gpt : \(3x^2-4x-7=2\left(x+3\right)\sqrt{2x-1}\)
gpt
\(4\sqrt{x+4}+\sqrt{16-3x}=x^2+4x+12\)
gpt
\(3x-1+\dfrac{x-1}{4x}=\sqrt{3x+1}\)
1, gpt:
\(3\sqrt{1+x}+3\sqrt{3-3x}=\sqrt{28x^2-12x+9}\)
2, giải hpt:
\(\left\{{}\begin{matrix}\dfrac{4}{2x+y}+\dfrac{1}{3x-y}=2\\4x+12y=7\left(2x+y\right)\left(3x-y\right)\end{matrix}\right.\).
gpt : a. \(x^2-7x=6\sqrt{x+5}-30\)
b. \(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3\left(x^2-x-1\right)}-\sqrt{x^2-3x-4}\)
\(GPT:2\sqrt{x+3}-\sqrt[3]{3x+5}=2\)
GPT :\(5\sqrt{x-1}-\sqrt{x+7}=3x-4\)
gpt : a) \(\frac{5x}{\sqrt{4-x^2}}+\frac{8}{x^2}+\frac{2x}{4-x^2}+\frac{5\sqrt{4-x^2}}{x}+4=0\)
b) \(\frac{2x}{\sqrt{8x^2+25}}+\frac{125}{x^2}-14=0\)
c) \(\left(x^3-3x+2\right)\sqrt{3x-2}-2x^3+6x^2-4x=0\)
d) \(\sqrt{x^2-x+6}+\frac{4}{x-1}=x^2+x\)
Gpt : a) \(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right)\left(x^2-3x+5\right)}=4-2x\)
b) \(\sqrt[4]{1-x}+\sqrt[4]{2-x}=\sqrt[4]{3-2x}\)
c) \(\sqrt{x+1}+\sqrt{x+10}=\sqrt{x+2}+\sqrt{x+5}\)
