Tìm ĐKXĐ:
a) \(\dfrac{3}{\sqrt{12x-1}}\)
b) \(\sqrt{\left(3x+2\right)\left(x-1\right)}\)
c) \(\sqrt{3x-2}\) .\(\sqrt{x-1}\)
d) \(\sqrt{\dfrac{-2\sqrt{6}+\sqrt{23}}{-x+5}}\)
Phân tích đa thức thành nhân tử
x^3+9x^2+27x+27
3\(\sqrt{3x^3}\)+18x^2+12\(\sqrt{3x}\)+8
\(\dfrac{1}{4}\)-x^2
Giải phương trình vô tỉ :
a) \(\left(\sqrt{x+3}-\sqrt{x-1}\right)\left(x^2+\sqrt{x^2+4x+3}\right)=2x\)
b) \(\sqrt{2x+4}-2\sqrt{2-x}=\frac{6x-4}{\sqrt{x^2+4}}\)
c) \(\sqrt{3x^2-4x+2}+\sqrt{3x+1}+\sqrt{2x-1}+6x^3-7x^2-3=0\)
d) \(\sqrt{x^2+15}=3x-2+\sqrt{x^2+8}\)
Giải các phương trình:
a,\(\sqrt{x+3+4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}=5}\)
b, \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)=4\)
2(2x-1)-3\(\sqrt{5x-6}\)=\(\sqrt{3x-8}\)
\(\left(\dfrac{7x+5}{x^2+3x+2}-\dfrac{2x-3}{x+2}-\dfrac{x-1}{x+1}\right):\dfrac{20-6\sqrt{x}}{3x+6}\)
GPT: \(2\sqrt{3x}-4\sqrt{3x}+27-3\sqrt{3x}\) = 0
tìm x
\(\sqrt{x^2+24}+1=3x+\sqrt{x^2+8}\)
Giải phương trình:
a) \(\sqrt{1-x^2}=\left(\frac{2}{3}-\sqrt{x}\right)^2\)
b) \(\sqrt{x^2+15}=3\sqrt[3]{x}+\sqrt{x^2+8}-2\)
c) \(x+\frac{3x}{\sqrt{1+x^2}}=1\)
d) \(3x+\sqrt{x^2+5}-\sqrt{x^2+12}-5=0\)
