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\(\Leftrightarrow2x+2+\sqrt{4x^2-16x+4}=6\sqrt{x}\)
\(\Leftrightarrow2x+2-5\sqrt{x}+\sqrt{4x^2-16x+4}-\sqrt{x}=0\)
\(\Leftrightarrow\frac{4x^2-17x+4}{2x+2+5\sqrt{x}}+\frac{4x^2-17x+4}{\sqrt{4x^2-16x+4}+\sqrt{x}}=0\)
\(\Leftrightarrow\left(4x^2-17x+4\right)\left(\frac{1}{2x+2+5\sqrt{x}}+\frac{1}{\sqrt{4x^2-16x+4}+\sqrt{x}}\right)=0\)
\(\Rightarrow4x^2-17x+4=0\Rightarrow\left[{}\begin{matrix}x=\frac{1}{4}\\x=4\end{matrix}\right.\)
Giải phương trình:
a) \(\sqrt{x+2}=\sqrt{2x+1}+x\sqrt{x+2}\)
b) \(2+\sqrt{3-8x}=6x+\sqrt{4x-1}\)
c) \(\sqrt{10x+1}+\sqrt{3x-5}=\sqrt{9x+4}+\sqrt{2x-1}\)
d) \(1+\sqrt{x^2+4x}=\sqrt{x^2-3x+3}+\sqrt{2x^2+x+2}\)
e) \(\sqrt{x^2+15}=3x-2+\sqrt{x^2+8}\)
f) \(\left(\sqrt{x+5}-\sqrt{x+2}\right)\left(1+\sqrt{x^2+7x+10}\right)=3\)
g) \(\sqrt{3x^2-7x+3}-\sqrt{x^2-2}=\sqrt{3x^2-5x-1}-\sqrt{x^2-3x+4}\)
h) \(\sqrt{2x^2+x-1}+\sqrt{3x^2+x-1}=\sqrt{x^2+4x-3}+\sqrt{2x^2+4x-3}\)
Giải phương trình:
1. \(x^4-6x^2-12x-8=0\)
2. \(\dfrac{x}{2x^2+4x+1}+\dfrac{x}{2x^2-4x+1}=\dfrac{3}{5}\)
3. \(x^4-x^3-8x^2+9x-9+\left(x^2-x+1\right)\sqrt{x+9}=0\)
4. \(2x^2.\sqrt{-4x^4+4x^2+3}=4x^4+1\)
5. \(x^2+4x+3=\sqrt{\dfrac{x}{8}+\dfrac{1}{2}}\)
6. \(\left\{{}\begin{matrix}4x^3+xy^2=3x-y\\4xy+y^2=2\end{matrix}\right.\)
7. \(\left\{{}\begin{matrix}\sqrt{x^2-3y}\left(2x+y+1\right)+2x+y-5=0\\5x^2+y^2+4xy-3y-5=0\end{matrix}\right.\)
8. \(\left\{{}\begin{matrix}\sqrt{2x^2+2}+\left(x^2+1\right)^2+2y-10=0\\\left(x^2+1\right)^2+x^2y\left(y-4\right)=0\end{matrix}\right.\)
\(a,2x^2-9x+3+\sqrt{3x^2-7x+1}=0\)
b)\(\sqrt{x+2}+\sqrt{3-x}=x^3+x^2-4x-1\)
c)\(\text{4x^3-9x^2+7x-(3x-1)\sqrt{3x-2}=0}\)
d)\(2\sqrt{x-1}+\sqrt{5x-1}=x^2+1\)
e)\(\sqrt{x+2}+\sqrt{5x+6}+2\sqrt{8x+9}=4x^2\)
f)\(3x^2-x+3=\sqrt{3x+1}+\sqrt{5x+4}\)
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 phương trình:
1) \(3x^2+4x-3=4x\sqrt{4x-3}\)
2) \(\sqrt{x^2+2x}+\sqrt{x+2}=\sqrt{x}+\sqrt{x^2+2x-2}\)
3) \(\sqrt{3x+8}-\sqrt{3x+5}=\sqrt{5x-4}-\sqrt{5x-7}\)
4) \(\sqrt{7-x^2+x\sqrt{x+5}}=\sqrt{3-2x-x^2}\)
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) \(\frac{x^2}{4-3\sqrt{x}}+8=3\left(x+2\sqrt{x}\right)\)
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 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 phương trình sau
a/ \(\left(4x-1\right)\sqrt{x^3+1}=2x^3+2x+1\)
b/ \(\left(x+1\right)\sqrt{x^2-2x+3}=x^2+1\)
c/ \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2+16}\)
d/ \(x^2+4x=\left(x+2\right)\sqrt{x^2-2x+4}\)
\(8\sqrt{x^2+\frac{3}{4}+\sqrt{4x^2-1}}=10\sqrt{x^2+\frac{3}{4}-\sqrt{x^2}+\frac{1}{2}}+7\)
