ĐKXĐ: \(x\ge1\)
\(\sqrt{3x-2}-2+\sqrt{x-1}-1=0\)
\(\Leftrightarrow\dfrac{3x-6}{\sqrt{3x-2}+2}+\dfrac{x-2}{\sqrt{x-1}+1}=0\)
\(\Leftrightarrow\left(x-2\right)\left(\dfrac{3}{\sqrt{3x-2}+2}+\dfrac{1}{\sqrt{x-1}+1}\right)=0\)
\(\Leftrightarrow x-2=0\)
Giải phương trình vô tỉ:
1/ \(\sqrt{x^2+12}+5=3x+\sqrt{x^2+15}\)
2/ \(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3\left(x^2-x+1\right)}-\sqrt{x^2-3x+4}\)
3/ \(\sqrt[5]{x-1}+\sqrt[3]{x+8}=-x^3+1\)
4/ \(\sqrt{5-x^6}+\sqrt[3]{3x^4-2}=1\)
Tìm x:
1, \(\sqrt{1-2x}+\sqrt{1+2x}=\sqrt{4+x}\)
2,\(\sqrt{3x+1}-\sqrt{2-x}=\sqrt{3x-2}\)
3, \(\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}=4\)
4, \(3x^2-6x-4=4\left(x-1\right)\sqrt{3x+1}\)
Tìm điều kiện xác định
\(A=\sqrt{x^2-5x+6}\)
\(B=\dfrac{x}{\sqrt{7x^2-8}}\)
\(C=\sqrt{-9x^2+6x-1}-\dfrac{1}{\sqrt{x^2+x+2}}\)
\(D=\sqrt{3-x^2}-\sqrt{\dfrac{2021}{3x+2}}\)
\(E=\sqrt{\dfrac{3x^2}{2x+1}-1}\)
\(F=\sqrt{25x^2-10x+1}+\dfrac{1}{1-5x}\)
Giải các phương trình sau:
a) \(x^3-x^2+2x=\sqrt{2x-1}+\sqrt{4x-3}\)
b) \(x^3-x^2+3x+13=4\left(\sqrt{x+3}+\sqrt{3x+1}\right)\)
c) \(x^3-4x^2+6x-1=\sqrt{2x-3}+2\sqrt{x-1}\)
d) \(x^3+4x^2+9x+9=2\sqrt{3x+4}+\sqrt{2x+3}\)
e) \(2x^2-4x+11=2\sqrt{3x-5}+3\sqrt{2x+5}\)
Giải các phương trình sau:
a) \(x^3-x^2+2x=\sqrt{2x-1}+\sqrt{4x-3}\)
b) \(x^3-x^2+3x+13=4\left(\sqrt{x+3}+\sqrt{3x+1}\right)\)
c) \(x^3-4x^2+6x-1=\sqrt{2x-3}+2\sqrt{x-1}\)
d) \(x^3+4x^2+9x+9=2\sqrt{3x+4}+\sqrt{2x+3}\)
e) \(2x^2-4x+11=2\sqrt{3x-5}+3\sqrt{2x+5}\)
\(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3\left(x^2-x-1\right)}-\sqrt{x^2-3x+4}\)
Giải các phương trình
a) \(\sqrt{2x+9}=\sqrt{5-4x}\)
b) \(\sqrt{2x-1}=\sqrt{x-1}\)
c) \(\sqrt{x^2+3x+1}=\sqrt{x+1}\)
d) \(\sqrt{2x^2-3}=\sqrt{4x-3}\)
1)giải pt: 1+\(\dfrac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
2)giải pt: \(\dfrac{x^2}{\sqrt{3x-2}}-\sqrt{3x-2}=1-x\)
Tìm x:
a)\(\dfrac{1}{3}\sqrt{x-1}+2\sqrt{4x-4}-12\sqrt{\dfrac{x-1}{25}}=\dfrac{29}{15}\)
b)\(\dfrac{3x-2}{\sqrt{x-1}}-\sqrt{x+1}=\sqrt{2x-3}\)
Rút gon A=\(\sqrt[3]{\dfrac{x^3-3x+\left(x^2-1\right)\sqrt{x^2-4}}{2}}+\sqrt[3]{\dfrac{x^3-3x-\left(x^2-1\right)\sqrt{x^2-4}}{2}}\)
