\(\frac{1}{x-4\sqrt{x}+2}\)
Những câu hỏi liên quan
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)
Đọc tiếp
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. \(\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right)\frac{\left(\sqrt{x}-1\right)^2}{2}\left(x\ge0,x\ne1\right)\)
Trả lời nhanh giúp mình với mình cần gấp lắm
Bài 1: Tính :
Csqrt{frac{3sqrt{3}-4}{2sqrt{3}+1}}-sqrt{frac{sqrt{3}+4}{5-2sqrt{3}}}
Bfrac{1}{sqrt{1}+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+frac{1}{sqrt{3}+sqrt{4}}+....+frac{1}{sqrt{99}+sqrt{100}}
Dsqrt{1+sqrt{3+sqrt{13+4sqrt{3}}}}+sqrt{1-sqrt{3-sqrt{13-4sqrt{3}}}}
Bài 2 : Cho Pleft(frac{1}{sqrt{x}-1}+frac{x-sqrt{x}+6}{x+sqrt{x}-2}right):left(frac{sqrt{x}+1}{sqrt{x}+2}+frac{x-sqrt{x}-2}{x+sqrt{x}+2}right)
a, Rút gọn P
b, Tìm GTNN
c, Tìm x để P.frac{x-1}{x^2+8x} -2
Đọc tiếp
Bài 1: Tính :
\(C=\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
\(B=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+....+\frac{1}{\sqrt{99}+\sqrt{100}}\)
\(D=\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Bài 2 : Cho \(P=\left(\frac{1}{\sqrt{x}-1}+\frac{x-\sqrt{x}+6}{x+\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}+2}+\frac{x-\sqrt{x}-2}{x+\sqrt{x}+2}\right)\)
a, Rút gọn P
b, Tìm GTNN
c, Tìm x để \(P.\frac{x-1}{x^2+8x}< -2\)
Bài 1: Tính :Csqrt{frac{3sqrt{3}-4}{2sqrt{3}+1}}-sqrt{frac{sqrt{3}+4}{5-2sqrt{3}}}Bfrac{1}{sqrt{1}+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+frac{1}{sqrt{3}+sqrt{4}}+....+frac{1}{sqrt{99}+sqrt{100}}Dsqrt{1+sqrt{3+sqrt{13+4sqrt{3}}}}+sqrt{1-sqrt{3-sqrt{13-4sqrt{3}}}}Bài 2 : Cho Pleft(frac{1}{sqrt{x}-1}+frac{x-sqrt{x}+6}{x+sqrt{x}-2}right):left(frac{sqrt{x}+1}{sqrt{x}+2}+frac{x-sqrt{x}-2}{x+sqrt{x}+2}right) a, Rút gọn P b, Tìm GTNNc, Tìm x để P.frac{x-1}{x^2+8x} -2
Đọc tiếp
Bài 1: Tính :
\(C=\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
\(B=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+....+\frac{1}{\sqrt{99}+\sqrt{100}}\)
\(D=\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Bài 2 : Cho \(P=\left(\frac{1}{\sqrt{x}-1}+\frac{x-\sqrt{x}+6}{x+\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}+2}+\frac{x-\sqrt{x}-2}{x+\sqrt{x}+2}\right)\)
a, Rút gọn P
b, Tìm GTNN
c, Tìm x để \(P.\frac{x-1}{x^2+8x}< -2\)
1. Rút gọn
P=\(2\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}:\left[\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}-\frac{1}{2}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2\right]\)
chứng minh rằng
a, \(\frac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\frac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}=1\)
b, \(\frac{1}{x+\sqrt{x}}+\frac{2\sqrt{x}}{x-1}-\frac{1}{x-\sqrt{x}}=\frac{2}{\sqrt[]{x}}\)
a, \(\frac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\frac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}\)
\(=\frac{2+\sqrt{3}}{2+\sqrt{\left(\sqrt{3}+1\right)^2}}+\frac{2-\sqrt{3}}{2-\sqrt{\left(\sqrt{3}-1\right)^2}}\)
\(=\frac{2+\sqrt{3}}{2+\sqrt{3}+1}+\frac{2-\sqrt{3}}{2-\sqrt{3}+1}\)
\(=\frac{2+\sqrt{3}}{3+\sqrt{3}}+\frac{2-\sqrt{3}}{3-\sqrt{3}}\)
\(=\frac{\left(2+\sqrt{3}\right)\left(3-\sqrt{3}\right)+\left(2-\sqrt{3}\right)\left(3+\sqrt{3}\right)}{\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)}\)
\(=\frac{6+\sqrt{3}-3+6-\sqrt{3}-3}{9-3}=\frac{6}{6}=1\)
b, \(\frac{1}{x+\sqrt{x}}+\frac{2\sqrt{x}}{x-1}-\frac{1}{x-\sqrt{x}}\)
\(=\frac{1}{\sqrt{x}\left(\sqrt{x}+1\right)}+\frac{2\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x-1}\right)}-\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(=\frac{\sqrt{x}-1+2x-\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}=\frac{2\left(x-1\right)}{\sqrt{x}\left(x-1\right)}=\frac{2}{\sqrt{x}}\)
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7 tháng 10 2019 lúc 12:48
Rút gọn biểu thức :
\(D=\frac{x+2+\sqrt{x^2+4}}{x+2-\sqrt{x^2-4}}+\frac{x+2-\sqrt{x^2}-4}{x+2+\sqrt{x^2}-4}\)
\(Q=\frac{1}{x^2-\sqrt{x}}:\frac{\sqrt{x}+1}{x\sqrt{x}+x+\sqrt{x}}\)
bài 5ĐK:x2,y1frac{36}{sqrt{x-2}}+frac{4}{sqrt{y-1}}28-4sqrt{x-2}-sqrt{y-1}..Leftrightarrowfrac{36}{sqrt{x-2}}+4sqrt{x-2}+frac{4}{sqrt{y-1}}+sqrt{y-1}28Áp dụng AM-GM ta có:frac{36}{sqrt{x-2}}+4sqrt{x-2}ge2sqrt{frac{144sqrt{x-2}}{sqrt{x-2}}}24frac{4}{sqrt{y-1}}+sqrt{y-1}ge2sqrt{frac{4sqrt{y-1}}{sqrt{y-1}}}4.Rightarrowfrac{36}{sqrt{x-2}}+4sqrt{x-2}+frac{4}{sqrt{y-1}}+sqrt{y-1}ge28.Dấu xảy ra khi frac{36}{sqrt{x-2}}4sqrt{x-2}Leftrightarrow x11left(nright).frac{4}{sqrt{y-1}}sqrt{y-1}Leftrightarrow y5...
Đọc tiếp
bài 5
ĐK:\(x>2,y>1\)
\(\frac{36}{\sqrt{x-2}}+\frac{4}{\sqrt{y-1}}=28-4\sqrt{x-2}-\sqrt{y-1}..\)\(\Leftrightarrow\frac{36}{\sqrt{x-2}}+4\sqrt{x-2}+\frac{4}{\sqrt{y-1}}+\sqrt{y-1}=28\)
Áp dụng AM-GM ta có:
\(\frac{36}{\sqrt{x-2}}+4\sqrt{x-2}\ge2\sqrt{\frac{144\sqrt{x-2}}{\sqrt{x-2}}}=24\)
\(\frac{4}{\sqrt{y-1}}+\sqrt{y-1}\ge2\sqrt{\frac{4\sqrt{y-1}}{\sqrt{y-1}}}=4.\)
\(\Rightarrow\frac{36}{\sqrt{x-2}}+4\sqrt{x-2}+\frac{4}{\sqrt{y-1}}+\sqrt{y-1}\ge28.\)
Dấu \(=\)xảy ra khi \(\frac{36}{\sqrt{x-2}}=4\sqrt{x-2}\Leftrightarrow x=11\left(n\right).\)
\(\frac{4}{\sqrt{y-1}}=\sqrt{y-1}\Leftrightarrow y=5\left(n\right).\)
Vậy \(x=11,y=5\)
<br class="Apple-interchange-newline"><div id="inner-editor"></div>x>2;y>1
Khi đó Pt ⇔36√x−2 +4√x−2+4√y−1 +√y−1=28
theo BĐT Cô si ta có 36√x−2 +4√x−2≥2.√36√x−2 .4√x−2=24
và 4√y−1 +√y−1≥2√4√y−1 .√y−1=4
Pt đã cho có VT>= 28 Dấu "=" xảy ra ⇔
36√x−2 =4√x−2⇔x=11
và 4√y−1 =√y−1⇔y=5
Đối chiếu với ĐK thì x=11; y=5 là nghiệm của PT
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Tìm điều kiện x để các biểu thức sau \(a)\frac{x}{x^2-4}+\sqrt{x-2}\\ b)\frac{\sqrt{x}}{\left|x\right|-1}\\ c)\frac{2}{\left|x\right|+4}+\sqrt{x^2-4}\\ d)\frac{1}{\sqrt{x-2\sqrt{x-1}}}\\ e)\sqrt{x^2-2x}+3\sqrt{4-x^2}\)
a) Để giá trị của biểu thức \(\frac{x}{x^2-4}+\sqrt{x-2}\)xác định được thì
\(\left\{{}\begin{matrix}x^2-4\ne0\\x-2\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\notin\left\{2;-2\right\}\\x\ge2\end{matrix}\right.\Leftrightarrow x>2\)
b) Để giá trị của biểu thức \(\frac{\sqrt{x}}{\left|x\right|-1}\) xác định được thì
\(\left\{{}\begin{matrix}x\ge0\\\left|x\right|-1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\left|x\right|\ne1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\notin\left\{1;-1\right\}\end{matrix}\right.\Leftrightarrow0\le x\ne1\)
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Rút gọn
a) \(\left(\frac{2+\sqrt{a}}{a+2\sqrt{a}+1}-\frac{\sqrt{a}-2}{a-1}\right)\left(\frac{a\sqrt{a}-\sqrt{a}-1}{\sqrt{a}}\right)\)
b) \(\left(\frac{\sqrt{x}+1}{x-4}-\frac{\sqrt{x}-1}{x+4\sqrt{x}+4}\right)\left(\frac{x\sqrt{x}+2x+4\sqrt{x}-8}{\sqrt{x}}\right)\)
Rút gọn A = \(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right) :\left(3+\frac{1}{\sqrt{x}-2}+\frac{2}{\sqrt{x}+1}\right)\)
a, Rút gọn A b , Tìm x thỏa mãn A > 1 c,Tính A với \(x=\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\)\(A=\frac{\sqrt{x}+1}{3\left(\sqrt{x}-1\right)}\)