ĐKXĐ: \(x\ge-2\)
\(\Leftrightarrow\left(x+2\right)\left(x+4\right)=3\sqrt{x+2}\)
Đặt \(\sqrt{x+2}=t\ge0\)
\(\Rightarrow t^2\left(t^2+2\right)=3t\)
\(\Leftrightarrow t\left(t^3+2t-3\right)=0\)
\(\Leftrightarrow t\left(t-1\right)\left(t^2+t+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}t=0\\t=1\end{matrix}\right.\) \(\Rightarrow x=\)
gpt:
\(a,\sqrt{2x+4}-2\sqrt{2-x}=\dfrac{6x-4}{\sqrt{x^2+4}}\)
b) \(\sqrt{\dfrac{6}{3-x}}+\sqrt{\dfrac{8}{2-x}}=6\)
Gpt: \(\sqrt[8]{1-x}+\sqrt[8]{1+x}+\sqrt[8]{1-x^2}=3\)
gpt:
1, (17-6x)\(\sqrt{3x-5}\) + (6x-7)\(\sqrt{7-3x}\) =2 + 8\(\sqrt{36x-9x^2-35}\)
2, \(\left(\dfrac{x-1}{x+2}\right)^2-\dfrac{15}{x^2-4}+4\left(\dfrac{x+1}{x-2}\right)^2=5\)
GPT :
a) \(\sqrt{x-2}+\sqrt{4-x}=x^2-6x+11\)
b) \(\sqrt{x^2+x-1}+\sqrt{-x^2+x+1}=x^2-x+2\)
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
\(x^2-3\sqrt[3]{3x-2}-12+\frac{1}{\sqrt{x}}=\frac{\sqrt{x}+8}{x}\)
gpt
\(28x^2+6x-27=18\sqrt{1-x^2}\)
gpt:
1, \(3\sqrt{3}\left(x^2+4x+2\right)-\sqrt{x+8}=0\)
2, \(x^2-x-2\sqrt{1+16x}=2\)
gpt:
1, 3\(\sqrt{3}\)(x2+4x+2)−\(\sqrt{x+8}\)=0
GPT : \(\sqrt{x^2-3x+2}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)
