ĐKXĐ: ...
\(\Leftrightarrow\frac{25\left(x-1\right)-\left(x+7\right)}{5\sqrt{x-1}+\sqrt{x+7}}=3x-4\)
\(\Leftrightarrow\frac{8\left(3x-4\right)}{5\sqrt{x-1}+\sqrt{x+7}}=3x-4\)
\(\Rightarrow\left[{}\begin{matrix}3x-4=0\\5\sqrt{x-1}+\sqrt{x+7}=8\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow5\left(\sqrt{x-1}-1\right)+\sqrt{x+7}-3=0\)
\(\Leftrightarrow\frac{5\left(x-2\right)}{\sqrt{x-1}+2}+\frac{x-2}{\sqrt{x+7}+3}=0\)
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. \(x^2-7x=6\sqrt{x+5}-30\)
b. \(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3\left(x^2-x-1\right)}-\sqrt{x^2-3x-4}\)
Gpt : 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) \(\sqrt{x+1}+\sqrt{x+10}=\sqrt{x+2}+\sqrt{x+5}\)
GPT
2x3-x2-3x+1=\(\sqrt{x^5+x^4+1}\)
gpt
\(4\sqrt{x+4}+\sqrt{16-3x}=x^2+4x+12\)
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:
x2 + \(\dfrac{9x^2}{\left(x+3\right)^2}\) = 7
ghpt:
\(\left\{{}\begin{matrix}2\sqrt{x+3y+2}-3\sqrt{y}=\sqrt{x+2}\\x^2-3x-4\sqrt{y}+10=0\end{matrix}\right.\)
\(GPT:2\sqrt{x+3}-\sqrt[3]{3x+5}=2\)
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) \(\sqrt{x^2-x+6}+\frac{4}{x-1}=x^2+x\)
