ĐKXĐ: x >= 1/2
Bình phương cả 2 vế ta được:
2x - 1 = (x + 1)2
<=> 2x - 1 = x2 + 1 + 2x
<=> x2 + 1 + 2x - 2x + 1 = 0
<=> x2 + 2 = 0
<=> x2 = -2
pt vô nghiệm
giải pt
a) \(\sqrt{x+2\sqrt{x-1}}+3\sqrt{x+8-6\sqrt{x-1}}=1-x\)
b) \(\sqrt{x\sqrt{x-1}-2x+2}+\sqrt{\left(x+3\right)\sqrt{x-1}-4x+4}=\sqrt{x-1}\)
c) \(\sqrt{14x+14\sqrt{14x-49}}+\sqrt{14x-14\sqrt{14x-49}}=14\)
d) \(\sqrt{2x-2\sqrt{2x-1}}-2\sqrt{2x+3-4\sqrt{2x-1}}+3\sqrt{2x+8-6\sqrt{2x-1}}=4\)
giải các PT sau :
a) \(\left|2x+3\right|-\left|x\right|+\left|x-1\right|=2x+4\)
b) \(\sqrt{x}-\dfrac{4}{\sqrt{x+2}}+\sqrt{x+2}=0\)
c) \(\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
d) \(x+\sqrt{x+\dfrac{1}{2}+\sqrt{x+\dfrac{1}{4}}}=4\)
e) \(\sqrt{4x+3}+\sqrt{2x+1}=6x+\sqrt{8x^2+10x+3}-16\)
f)\(\sqrt[3]{x-2}+\sqrt{x+1}=3\)
GIÚP MÌNH VỚI MÌNH ĐANG CẦN GẤP
\(\sqrt{x-\sqrt{x^2-1}}+\sqrt{x+\sqrt{x^2-1}}=2\)
\(2\left(1-x\right)\sqrt{x^2+2x-1}=x^2-2x-1\)
giải dùm mình với ạ <3
1. \(\sqrt{x+2}+x^2-x-2\le\sqrt{3x-2}\)
2. \(\sqrt{2x+1}+\sqrt[4]{2x-1}< \sqrt{x-1}+\sqrt{x^2-2x+3}\)
3. \(\sqrt[3]{3-2x}+\frac{5}{\sqrt{2x-1}}-2x\le6\)
4. \(\left(x+3\right)\sqrt{x+1}+\left(x-3\right)\sqrt{1-x}+2x=0\)
giải pt
a) \(\sqrt{x+1}+\sqrt{x}+2\sqrt{x^2+x}=1-2x\)
b) \(\sqrt{x-2}-\sqrt{x+2}=2\sqrt{x^2-4}-2x+2\)
c) \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-16\)
d) \(2\sqrt{x}\left(\sqrt{x+1}-2\sqrt{x}\right)+\sqrt{x+1}+\sqrt{x}=1-6x\)
e) \(x^2+2x+\sqrt{x+3}+2x\sqrt{x+3}=9\)
giải pt
a) \(\sqrt{2x+3}+\sqrt{4-x}=6x-3\left(\sqrt{2x+3}-\sqrt{4-x}\right)^2-10\)
b) \(\sqrt{4x+1}+2\sqrt{1-x}+10\sqrt{-4x^2+3x+1}=13\)
c) \(\left(x^2+1\right)^2=13-x\sqrt{2x^2+4}\)
d) \(\left(\sqrt{x+1}+\sqrt{x-1}\right)^2-3=\frac{1}{\sqrt{x+1}-\sqrt{x-1}}\)
e) \(\left(\frac{2x-3}{\sqrt{x^2-1}}+2\right)\left(\frac{1}{\sqrt{x-1}}-\frac{1}{\sqrt{x+1}}\right)=\frac{1}{x^2-1}\)
giải pt
a) \(2\sqrt{\frac{x}{x-1}}-\sqrt{\frac{x-1}{x}}=\frac{5x-2}{x}\)
b) \(3\sqrt{\frac{2x}{x-1}}+4\sqrt{\frac{x-1}{2x}}=\frac{5x-3}{2x}+9\)
c) \(\sqrt{\frac{x}{3-2x}}+5\sqrt{\frac{3-2x}{x}}=\frac{12-9x}{x}+6\)
d) \(\frac{x-1}{x}-2\sqrt{\frac{x-1}{x}}=3\)
e) \(\sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{3}{\sqrt{2}}\)
f) \(\sqrt{x-\frac{1}{x}}=\frac{1}{\sqrt{x}}-\sqrt{x}\)
1. Giải các phương trình sau:
a)\(\sqrt[4]{x-\sqrt{x^2-1}}+\sqrt[]{x+\sqrt{x^2-1}}=2\)
b)\(x^2-x-\sqrt{x^2-x+13}=7\)
c)\(x^2+2\sqrt{x^2-3x+1}=3x+4\)
d)\(2x^2+5\sqrt{x^2+3x+5}=23-6x\)
e)\(\sqrt{x^2+2x}=-2x^2-4x+3\)
f)\(\sqrt{\left(x+1\right)\left(x+2\right)}=x^2+3x+4\)
2. Giải các bất phương trình sau:
1)\(\sqrt{x^2-4x+5}\ge2x^2-8x\)
2)\(2x^2+4x+3\sqrt{3-2x-x^2}>1\)
3)\(\dfrac{\sqrt{-3x+16x-5}}{x-1}\le2\)
4)\(\sqrt{x^2-3x+2}+\sqrt{x^2-4x+3}\ge2\sqrt{x^2-5x+4}\)
5)\(\dfrac{9x^2-4}{\sqrt{5x^2-1}}\le3x+2\)
Giải các phương trình sau
a/ \(\sqrt{\dfrac{1-x}{x}}=\dfrac{2x+x^2}{1+x^2}\)
b/\(\sqrt[3]{x+2}+\sqrt[3]{x+1}=\sqrt[3]{2x^2}+\sqrt[3]{2x^2+1}\)
c/ \(\sqrt{x+2}+\sqrt{4-x}=2x^2-5x-1\)
giải pt
a) \(3\sqrt{x}+\frac{3}{2\sqrt{x}}=2x+\frac{1}{2x}-7\)
b) \(5\sqrt{x}+\frac{5}{2\sqrt{x}}=2x+\frac{1}{2x}+4\)
c) \(\sqrt{2x^2+8x+5}+\sqrt{2x^2-4x+5}=6\sqrt{x}\)
d) \(x+1+\sqrt{x^2-4x+1}=3\sqrt{x}\)
e) \(x^2+2x\sqrt{x-\frac{1}{x}}=3x+1\)
f) \(x^2-6x+x\sqrt{\frac{x^2-6}{x}}-6=0\)
g) \(\frac{3x^2}{3+\sqrt{x}}+6+2\sqrt{x}=5x\)
h) \(\frac{x^2}{4-3\sqrt{x}}+8=3\left(x+2\sqrt{x}\right)\)
