ĐKXĐ: \(\sqrt{5}-\sqrt{3}x>=0\)
\(\Leftrightarrow x\sqrt{3}< =\sqrt{5}\)
hay \(x< =\sqrt{\dfrac{5}{3}}\)
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27 tháng 5 2021 lúc 22:16
1, \(K=\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
2, \(\sqrt{x-3}-2.\sqrt{x^2-3x}=0\)
3, \(\dfrac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}\)
4, \(x-5\sqrt{x}+4=0\)
1) x-\(7\sqrt{x-3}\) -9=0 2) \(\sqrt{x+3}\) =5-\(\sqrt{x-2}\) 3) \(\sqrt{x-4\sqrt{x+4}}\) =3 4) \(\sqrt{8-\dfrac{2}{3}x}-5\sqrt{2}\) =0 5) \(\sqrt{x^2-4x+4}\) =2-x
1, \(\sqrt{x-1}+\sqrt{x-4}=5\)
2, \(2x-7\sqrt{x}+5=0\)
3, \(\sqrt{2x+1}+\sqrt{x-3}=2\sqrt{x}\)
4, \(x-4\sqrt{x}+2021\sqrt{x-4}+4=0\)
5, \(\sqrt{2x-3}-\sqrt{x+1}=7\left(4-x\right)\)
1. sqrt{x-2sqrt{x-1}}+sqrt{x+3-4sqrt{x-1}}left(2 x 5right)2. frac{6}{1-sqrt{3}}-frac{3sqrt{3}-1}{sqrt{3}+1}+sqrt{3}3. sqrt{29-12sqrt{5}+sqrt{24-8sqrt{3}}}4. sqrt{frac{4}{9-4sqrt{5}}}-sqrt{frac{4}{9+4sqrt{5}}}5. 5sqrt{frac{1}{5}}+frac{1}{2}sqrt{x}-frac{5}{4}sqrt{frac{4}{5}+sqrt{5}}6. frac{6-sqrt{6}}{sqrt{6}-1}-9sqrt{frac{2}{3}}-frac{4}{2-sqrt{6}}7. left(frac{sqrt{x}-2}{x-1}-frac{sqrt{x}+2}{x+2sqrt{x}+1}right)frac{left(sqrt{x}-1right)^2}{2}left(xge0,xne1right)
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1. \(\sqrt{x-2\sqrt{x-1}}+\sqrt{x+3-4\sqrt{x-1}}\left(2< x< 5\right)\)
2. \(\frac{6}{1-\sqrt{3}}-\frac{3\sqrt{3}-1}{\sqrt{3}+1}+\sqrt{3}\)
3. \(\sqrt{29-12\sqrt{5}+\sqrt{24-8\sqrt{3}}}\)
4. \(\sqrt{\frac{4}{9-4\sqrt{5}}}-\sqrt{\frac{4}{9+4\sqrt{5}}}\)
5. \(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{x}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\)
6. \(\frac{6-\sqrt{6}}{\sqrt{6}-1}-9\sqrt{\frac{2}{3}}-\frac{4}{2-\sqrt{6}}\)
7. \(\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right)\frac{\left(\sqrt{x}-1\right)^2}{2}\left(x\ge0,x\ne1\right)\)
1.\(x\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}=\frac{3}{2}\sqrt{\frac{x}{x+\sqrt{x}}}\)
2.\(\sqrt{x-2+\sqrt{2x-5}}+\sqrt{x+2+3\sqrt{2x-5}}=7\sqrt{2}\)
3.\(\sqrt[4]{x}+\sqrt[4]{17-x}=3\)
4.\(\sqrt[3]{x+1}-\sqrt[3]{x-1}=\sqrt[6]{x^2-1}\)
5.\(\sqrt[3]{2x-1}=x\sqrt[3]{16}-\sqrt[3]{2x+1}\)
Rút gọn(dfrac{sqrt{x}}{3+sqrt{x}}+dfrac{2x}{9-x}):(dfrac{sqrt{x}-1}{x-3sqrt{x}}-dfrac{2}{sqrt{x}})(dfrac{sqrt{x}-2}{sqrt{x}+5}+dfrac{sqrt{x}}{sqrt{x}-5}+dfrac{x+9}{25-x}):dfrac{1-sqrt{x}}{5+sqrt{x}}(dfrac{1}{x-4}-dfrac{1}{x-4sqrt{x}+4}):dfrac{sqrt{x}}{2sqrt{x}-x}
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Rút gọn
(\(\dfrac{\sqrt{x}}{3+\sqrt{x}}\)+\(\dfrac{2x}{9-x}\)):(\(\dfrac{\sqrt{x}-1}{x-3\sqrt{x}}-\dfrac{2}{\sqrt{x}}\))
(\(\dfrac{\sqrt{x}-2}{\sqrt{x}+5}+\dfrac{\sqrt{x}}{\sqrt{x}-5}+\dfrac{x+9}{25-x}\)):\(\dfrac{1-\sqrt{x}}{5+\sqrt{x}}\)
(\(\dfrac{1}{x-4}-\dfrac{1}{x-4\sqrt{x}+4}\)):\(\dfrac{\sqrt{x}}{2\sqrt{x}-x}\)
Aleft(sqrt{5}-sqrt{2}right)^2-frac{9}{sqrt{10}-1}+sqrt{90}Bsqrt{2}left(3sqrt{2}+sqrt{3-sqrt{5}}right)-sqrt{5}Cleft(frac{5-sqrt{5}}{sqrt{5}-1}-frac{sqrt{5}+1}{5+sqrt{5}}right):frac{sqrt{5}+1}{sqrt{5}}Dfrac{xsqrt{y}-ysqrt{x}+sqrt{x}-sqrt{y}}{1+sqrt{xy}}:frac{x+2sqrt{xy}+y}{left(sqrt{x}+sqrt{y}right)^3left(x+yright)}vớix,y0TÍNH HOẶC RÚT GỌN
Đọc tiếp
\(A=\left(\sqrt{5}-\sqrt{2}\right)^2-\frac{9}{\sqrt{10}-1}+\sqrt{90}\)\(B=\sqrt{2}\left(3\sqrt{2}+\sqrt{3-\sqrt{5}}\right)-\sqrt{5}\)\(C=\left(\frac{5-\sqrt{5}}{\sqrt{5}-1}-\frac{\sqrt{5}+1}{5+\sqrt{5}}\right):\frac{\sqrt{5}+1}{\sqrt{5}}\)\(D=\frac{x\sqrt{y}-y\sqrt{x}+\sqrt{x}-\sqrt{y}}{1+\sqrt{xy}}:\frac{x+2\sqrt{xy}+y}{\left(\sqrt{x}+\sqrt{y}\right)^3\left(x+y\right)}vớix,y>0\)
TÍNH HOẶC RÚT GỌN
thực hiện phép tínhsqrt{left(4-sqrt{5}right)^2}+sqrt{5+2sqrt{5}+1}giải phương trìnhsqrt{x-3}6sqrt{left(x-3right)^2}12rút gọn biểu thứca) Pleft(dfrac{3-xsqrt{x}}{3-sqrt{x}}+sqrt{x}right).left(dfrac{3-sqrt{x}}{3-x}right) (với x≥0 ; x≠3; x≠9b) Pleft(dfrac{1}{sqrt{x}+1}-dfrac{1}{x+sqrt{x}}right)divdfrac{x-sqrt{x}+1}{xsqrt{x}+1} (x 0)c) Asqrt{3x-1}+3.sqrt{12x-4}-sqrt{6^2.left(3x-1right)}+sqrt{5} với x≥ dfrac{1}{3}d) Aleft(dfrac{asqrt{a}-1}{a-sqrt{a}}-dfrac{asqrt{a}+1}{a+sqrt{a}}right):dfrac{a+2}{a...
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thực hiện phép tính
\(\sqrt{\left(4-\sqrt{5}\right)^2}+\sqrt{5+2\sqrt{5}+1}\)
giải phương trình
\(\sqrt{x-3}=6\)
\(\sqrt{\left(x-3\right)^2}=12\)
rút gọn biểu thức
a) \(P=\left(\dfrac{3-x\sqrt{x}}{3-\sqrt{x}}+\sqrt{x}\right).\left(\dfrac{3-\sqrt{x}}{3-x}\right)\) (với x≥0 ; x≠3; x≠9
b) \(P=\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{1}{x+\sqrt{x}}\right)\div\dfrac{x-\sqrt{x}+1}{x\sqrt{x}+1}\) (x >0)
c) \(A=\sqrt{3x-1}+3.\sqrt{12x-4}-\sqrt{6^2.\left(3x-1\right)}+\sqrt{5}\) với x≥ \(\dfrac{1}{3}\)
d) \(A=\left(\dfrac{a\sqrt{a}-1}{a-\sqrt{a}}-\dfrac{a\sqrt{a}+1}{a+\sqrt{a}}\right):\dfrac{a+2}{a-2}\) với a>0,a≠1, a≠ \(\pm\)2
Giải các phương trình sau :
1/\(\sqrt{x+2+4\sqrt{x-2}}=5\)
2/\(\sqrt{x+3+4\sqrt{x-1}}=2\)
3/\(\sqrt{x+\sqrt{2x-1}}=\sqrt{2}\)
4/\(\sqrt{x-2+\sqrt{2x-5}}=3\sqrt{2}\)
10 tháng 10 2023 lúc 20:24
tìm ĐKXĐ
1, \(\sqrt{6x+1}\)
2,\(\dfrac{\sqrt{3}-4}{\sqrt{3x-5}}\)
3, \(\sqrt{\dfrac{2\sqrt{15}-\sqrt{59}}{x-7}}\)
4,\(\sqrt{\dfrac{-3x}{1-\sqrt{2}}}\)
5, \(\sqrt{\sqrt{5}-\sqrt{3}x}\)