Giải bất phương trình :
a, \(\sqrt{5x^2+14x+9}-\sqrt{x^2-x-20}\dfrac{< }{ }5\sqrt{x+1}\)
b, \(2x\sqrt{x}+\dfrac{5-4x}{\sqrt{x}}\dfrac{>}{ }\sqrt{x+\dfrac{10}{x}-2}\)
c, \(\sqrt{3x+1}-\sqrt{6-x}+3x^2-14x-8< 0\)
Giải phương trình
(3x + 1)\(\sqrt{2x^2+1}\) = 5x2 + \(\dfrac{3}{2}\)x - 3
giải phương trình
a, \(\sqrt{1+x}-\sqrt{8-x}+\sqrt{\left(1+x\right)\left(8-x\right)}=3\)
b, \(\sqrt{3x^2+5x+8}-\sqrt{3x^2+5x+1}=1\)
c, \(2x^2+4x=\sqrt{\dfrac{x+3}{2}}\)
d, \(2\left(x^2-3x+2\right)=3\sqrt{x^3+8}\)
e, \(729x^4+8\sqrt{1-x^2}=36\)
f, \(7x^2-10x+14=5\sqrt{x^4+4}\)
g, \(x^3+3x^2-3\sqrt[3]{3x+5}=1-3x\)
h, \(\sqrt{4-3\sqrt{10-3x}}=x-2\)
i, \(\sqrt{x-1}+\sqrt{x^2-1}=\sqrt{x^2-5x+4}\)
Giải hệ phương trình:
\(\left\{{}\begin{matrix}\left(x^2-1\right)^2+3=\dfrac{6x^5y}{x^2+2}\\3y-x=\sqrt{\dfrac{4x-3x^2y-9xy^2}{x+3y}}\end{matrix}\right.\)
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) \(\sqrt[3]{x^2+5x^1}-1=\sqrt{\dfrac{5x^2-2}{6}}\)
b) \(\dfrac{1}{\sqrt{2x+1}-\sqrt{3x}}=\dfrac{\sqrt{3x+2}}{1-x}\)
\(x^2+x\sqrt{2\text{x}-\dfrac{3}{x}}=1+x\sqrt{x-\dfrac{2}{x}}\)
Giải phương trình
Giải phương trình: \(\sqrt{x}\) + \(\sqrt{1-x}\) = 1 + \(\dfrac{2}{3}\sqrt{x-x^2}\)
Giải phương trình: \(\left(\sqrt{4x^4-12x^3+9x^2+16}-2x^2+3x\right)\left(\sqrt{x+3}+\sqrt{x-1}\right)=8\)