ĐKXĐ: \(x\ge2\)
\(\Leftrightarrow\frac{-3}{\sqrt{x-2}+\sqrt{x+1}}=\frac{x-4}{\sqrt{2x-1}+\sqrt{x+3}}\)
- Nếu \(x\ge4\Rightarrow\left\{{}\begin{matrix}VT< 0\\VP\ge0\end{matrix}\right.\) pt vô nghiệm
- Nếu \(2\le x< 4\) ta thấy:
\(\left\{{}\begin{matrix}x-2< 2x-1\\x+1< x+3\end{matrix}\right.\) \(\Rightarrow\sqrt{x-2}+\sqrt{x+1}< \sqrt{2x-1}+\sqrt{x+3}\)
Mà \(-3< x-4< 0\Rightarrow\frac{-3}{\sqrt{x-2}+\sqrt{x+3}}< \frac{x-4}{\sqrt{2x-1}+\sqrt{x+3}}\)
Tóm lại pt vô nghiệm
Giải pt:
a) \(\sqrt{2x^2-3}\)=\(\sqrt{4x-3}\)
b) \(\sqrt{2x-1}\)=\(\sqrt{x-1}\)
c) \(\sqrt{x^2-x-6}\)=\(\sqrt{x-3}\)
d) \(\sqrt{x^2-x}\)=\(\sqrt{3x-5}\)
Giúp em với, anh thịnh giúp em xíu á
giải pt sau
1, \(\sqrt{5-2x}=6\)
2,\(\sqrt{2-x}-\sqrt{x+1}=0\)
3, \(\sqrt{4x^2+4x+1}=6\)
4,\(\sqrt{x^2-10x+25}=x-2\)
1,
A=\(3\sqrt{8}-\sqrt{50}-\sqrt{\sqrt{2}-1}\)
B=2\(\dfrac{2}{x-1}\sqrt{\dfrac{x^2-2x+1}{4x^2}}\) với 0<x<1
2,Giải pt
\(\sqrt{x^2-3x+2}+\sqrt{x+2}=\sqrt{x+2}+\sqrt{x^2+2x+3}\)
Giải pt : a) \(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3\left(x^2-x-1\right)}-\sqrt{x^2-3x+4}\)
b) \(\left(x-1\right)\sqrt{x^2+5}+x=x^2+1\)
c)\(\sqrt{x+2}+2x-10=\sqrt{2x-3}\)
d)\(\sqrt{2x-3}-\sqrt{x}=2x-6\)
e) \(\sqrt{4x^2+5x+1}-2\sqrt{x^2-x+1}=9x-3\)
Giải PT: \(\sqrt{2x^4-3x^2+1}+\sqrt{2x^4-x^2}=4x-3\)
Giải pt
a.\(x+\sqrt{x+\dfrac{1}{2}+\sqrt{X+\dfrac{1}{4}}}=4\)
b.\(\sqrt{2x+4-6\sqrt{2x-5}}+\sqrt{2x-4+2\sqrt{2x-5}}=4\)
1)giải pt: 1+\(\dfrac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
2)giải pt: \(\dfrac{x^2}{\sqrt{3x-2}}-\sqrt{3x-2}=1-x\)
Giải pt sau
a,\(^{x^2-6x+26=6\sqrt{2x+1}}\)
b,\(x^2+2x\sqrt{x-\dfrac{1}{x}}=3x+1\)
giải pt \(\sqrt{x+2-3\sqrt{2x-5}}+\sqrt{x-2+\sqrt{2x-5}}=2\sqrt{2}\)
