ĐK : \(x\ge4\)
\(\sqrt{x+4\sqrt{x-4}}=2\)
\(\Leftrightarrow\sqrt{x-4+4\sqrt{x-4}+4}=2\)
\(\Leftrightarrow\sqrt{\left(\sqrt{x-4}+2\right)^2}=2\)
\(\Leftrightarrow\left|\sqrt{x-4}+2\right|=2\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-4}+2=-2\\\sqrt{x-4}+2=2\end{matrix}\right.\Leftrightarrow x=4\)
Giải các phương trình sau:
a)\(\sqrt[3]{9-x}+\sqrt[3]{7+x}=4\)
b)\(\sqrt{x-1}\cdot\sqrt[4]{x^2-4}=\sqrt{x-2}\cdot\sqrt[4]{x^2-1}\)
c)\(\sqrt[4]{9-x^2}+\sqrt{x^2-1}-2\sqrt{2}=\sqrt[6]{x-3}\)
giải pt
a.\(2\sqrt{x-4}-\dfrac{1}{3}\sqrt{9x-36}=4-\sqrt{x-4}\)
b.\(3\sqrt{x-2}-\sqrt{x^2-4}=0\)
c.\(\sqrt{3x^2-18x+28}+\sqrt{4x^2-24x+45}=-5-x^2+6x\)
Rút gọn:
\(A=\dfrac{\sqrt[3]{x^4}+\sqrt[3]{x^2y^2}+\sqrt[3]{y^4}}{\sqrt[3]{x^2}+\sqrt[3]{xy}+\sqrt[3]{y^2}}\)
\(B=\dfrac{\sqrt[3]{xy}\left(\sqrt[3]{y^2}-\sqrt[3]{x^2}\right)+\left(\sqrt[3]{x^4}-\sqrt[3]{y^4}\right)}{\sqrt[3]{x^4}+\sqrt[3]{x^2y^2}-\sqrt[3]{x^3y}}.\sqrt[3]{x^2}\)
\(C=\left(\dfrac{x\sqrt[3]{x}-2x\sqrt[3]{y}+\sqrt[3]{x^2y^2}}{\sqrt[3]{x^2}-\sqrt[3]{xy}}+\dfrac{\sqrt[3]{x^2y}-\sqrt[3]{xy^2}}{\sqrt[3]{x}-\sqrt[3]{y}}\right).\dfrac{1}{\sqrt[3]{x^2}}\)
Giải phương trình
a) \(\sqrt{x^2-2x+4}=2x-2\)
b) \(\sqrt{x+2\sqrt{x-1}}=2\)
c) \(\sqrt{2x^2-2x+1}=2x-1\)
d) \(\sqrt{x+4\sqrt{x-4}}=2\)
rút gọn :
a, \(\sqrt{x+4\sqrt{ }X-4}+\sqrt{x-4\sqrt{ }x-4}vớix>=8\)
b,\(\sqrt{2x-1+2\sqrt{ }x^2-x}+\sqrt{2x-1-2}\sqrt{x^2}-x\)
c, \(\dfrac{\sqrt{x-2\sqrt{x+1}}}{x+2\sqrt{ }x+1}\left(x>=0\right)\)
d, \(\dfrac{x-1}{\sqrt{ }y-1}\cdot\sqrt{\dfrac{\left(y-2\sqrt{y+1}\right)^2}{\left(x-1\right)^4}}\)
Rút gọn
a) \(\sqrt{\sqrt{2\sqrt{6}+6+2\sqrt{2}+2\sqrt{3}}-\sqrt{5+2\sqrt{6}}}\)
b) \(\sqrt{x^2-6x+9}-\dfrac{x^2-9}{\sqrt{9-6x+x^2}}\)
c) \(\dfrac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\dfrac{1}{\sqrt{x-1}}\right)\)
d) Rút gọn \(A=\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\)với \(2\le x\le4\)
1/ Thu gọn các biểu thức:
A=\(\sqrt{\dfrac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\dfrac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
B=\(\dfrac{x\sqrt{x}-2x+28}{x-3\sqrt{x}-4}-\dfrac{\sqrt{x}-4}{\sqrt{x}+1}+\dfrac{\sqrt{x}+8}{4-\sqrt{x}}\)
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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, \(3x^2-6x-4=4\left(x-1\right)\sqrt{3x+1}\)
Giải phương trình:
a)\(\sqrt{x^2+2x\sqrt{3}+3}=\sqrt{3}+x\)
b)\(\sqrt{x-3+2\sqrt{x-4}}=2\sqrt{x-4}+1\)
