giải phương trình
\(\text{x}^2-4=3\sqrt{\text{x}^3-4\text{x}}\)
\(9\text{x}+17=6\sqrt{8\text{x}-1}+4\sqrt{\text{x}+3}\)
\(\sqrt{2\text{x}-1}+\text{x}=\sqrt{\text{x}}+\sqrt{\text{x}^2-\text{x}+1}\)
\(2\sqrt{\text{x}^2-\text{x}+1}+\sqrt{\text{x}^2+\text{x}+1}=\sqrt{\text{x}^4+\text{x}^2+1}+2\)
Giải phương trình sau:
\(1,\sqrt{x-2}-\sqrt{x+1}=\sqrt{2\text{x}-1}-\sqrt{x+3}\)
\(2,x^2-6\text{x}+26=6\sqrt{2\text{x}+1}\)
\(3,\left(\sqrt{x+5}-\sqrt{x-2}\right)\left(1+\sqrt{x^2+7\text{x}+10}\right)=3\)
4,\(\sqrt[3]{x-4}-\sqrt{9-x}=-1\)
5,\(\left(x+1\right)\sqrt{16\text{x}+17}=8\text{x}^2-15\text{x}-23\)
Giúp mình với ạ mình đang cần gấp <3
\(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right)\left(x^2-3\text{x}+5\right)}=4-2\text{x}\)
Gpt: a) \(\sqrt[4]{3\left(x+5\right)}-\sqrt[4]{11-x}=\sqrt[4]{13+x}-\sqrt[4]{3\left(3-x\right)}\)
b) \(\frac{1+2\sqrt{x}-x\sqrt{x}}{3-x-\sqrt{2-x}}=2\left(\frac{1+x\sqrt{x}}{1+x}\right)\) c) \(\sqrt{x+1}+\frac{4\left(\sqrt{x+1}+\sqrt{x-2}\right)}{3\left(\sqrt{x-2}+1\right)^2}=3\)
d) \(\sqrt{\frac{x-2}{x+1}}+\frac{x+2}{\left(\sqrt{x+2}+\sqrt{x-2}\right)^2}=1\) e) \(2x+1+x\sqrt{x^2+2}+\left(x+1\right)\sqrt{x^2+2x+2}=0\)
f) \(\sqrt{2x+3}\cdot\sqrt[3]{x+5}=x^2+x-6\)
giải pt :
a) \(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)
b0 \(4\sqrt{x+1}=x^2-5x+14\)
c) \(2x+3\sqrt{4-5x}+\sqrt{x+2}=8\)
d) \(\dfrac{x^2+x}{\sqrt{x^2+x+1}}=\dfrac{2-x}{\sqrt{x-1}}\)
gpt : a) \(\frac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\frac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
b) \(\sqrt[3]{x+1}+\sqrt[3]{x+2}+\sqrt[3]{x+3}=0\)
c) \(\sqrt[4]{1-x^2}+\sqrt[4]{1+x}+\sqrt[4]{1-x}=3\)
Giải các phương trình sau:
1. \(\sqrt{x^2-\dfrac{1}{4}+\sqrt{x^2+x+\dfrac{1}{4}}}=\dfrac{1}{2}\left(2x^3+x^2+2x+1\right)\)
2. \(x^2+4x+7=\left(x+4\right)\sqrt{x^2+7}\)
3. \(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)
4. \(\sqrt{x^2-3x+2}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)
5. \(x=\left(\sqrt{x}+2\right)\left(1-\sqrt{1-\sqrt{x}}\right)\)
6. \(2\sqrt[3]{2x-1}=x^3+1\)
7. \(\sqrt{x-\dfrac{1}{x}}+\sqrt{1-\dfrac{1}{x}}=x\)
1) \(2\sqrt{x+3}=x-1+4\sqrt{2x-1}\)
2) \(\sqrt[4]{x-1}+\sqrt[4]{5-x}=2\)
3) \(\sqrt[3]{1-2x}+\sqrt{x+3}=1\)
4) \(\dfrac{\sqrt{x}}{1+\sqrt{1-x}}=x^2-2x+2\)
giải hệ pt:
(1)\(\left\{{}\begin{matrix}2\text{x}+2y+2\text{x}y=10\\x^2+y^2=5\end{matrix}\right.\)
(2)\(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y}=3\\\sqrt{xy}=2\end{matrix}\right.\)
(3)\(\left\{{}\begin{matrix}x-y=1\\x.y=6\end{matrix}\right.\)
(4)\(\left\{{}\begin{matrix}|x|+y=3\\2|x|-y=3\end{matrix}\right.\)