\(2\dfrac{3}{7}\) của 63 là
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1,( 2x - 7 )3 = \(\dfrac{26}{63}\)
2,( 7 - 3 x )2 = \(\dfrac{25}{144}\)
3,| 2 x - 3 = x + 1 |
4,| 3x + 1 | = 5
2: =>(3x-7)^2=25/144=(5/12)^2
=>3x-7=5/12 hoặc 3x-7=-5/12
=>3x=5/12+7=89/12 hoặc 3x=7-5/12=79/12
=>x=89/36 hoặc x=79/36
3:Sửa đề: |2x-3|=|x+1|
=>2x-3=x+1 hoặc 2x-3=-x-1
=>x=4 hoặc 3x=2
=>x=2/3 hoặc x=4
4: =>3x+1=5 hoặc 3x+1=-5
=>3x=4 hoặc 3x=-6
=>x=-2 hoặc x=4/3
1: =>\(2x-7=\sqrt[3]{\dfrac{26}{63}}\)
=>\(2x=\sqrt[3]{\dfrac{26}{63}}+7\)
=>\(x=\dfrac{1}{2}\cdot\left(\sqrt[3]{\dfrac{26}{63}}+7\right)\)
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\(\dfrac{2}{3}x+\dfrac{2}{15}x+\dfrac{2}{35}x+\dfrac{2}{63}x+\dfrac{99}{x}=-\dfrac{3}{7}\)
=>x(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9)+99/x=-3/7
=>8/9x+99/x=-3/7
\(\Leftrightarrow\dfrac{8x}{9}+\dfrac{99}{x}=\dfrac{-3}{7}\)
\(\Leftrightarrow\dfrac{8x^2+99\cdot9}{9x}=\dfrac{-3}{7}\)
\(\Leftrightarrow-56x^2-6237=27x\)
hay \(x\in\varnothing\)
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\(A=\sqrt{28}-\sqrt{63}+\dfrac{7+\sqrt{7}}{\sqrt{7}}-\sqrt{\left(\sqrt{7}+1\right)^2}\)
\(B=\left(\dfrac{1}{\sqrt{x}+3}+\dfrac{1}{\sqrt{x}-3}\right)\dfrac{4\sqrt{x}+12}{\sqrt{x}}\) (ĐK x>0; x\(\ne9\))
a)Rút gọn A và B
b) Tìm các giá trị của x để giá trị biểu thức A lớn hơn giá trị biểu thức B
a) \(A=\sqrt{28}-\sqrt{63}+\dfrac{7+\sqrt{7}}{\sqrt{7}}-\sqrt{\left(\sqrt{7}+1\right)^2}\)
\(=2\sqrt{7}-3\sqrt{7}+\dfrac{\sqrt{7}\left(\sqrt{7}+1\right)}{\sqrt{7}}-\left|\sqrt{7}+1\right|\)
\(=-\sqrt{7}+\sqrt{7}+1-\sqrt{7}-1=-\sqrt{7}\)
\(B=\left(\dfrac{1}{\sqrt{x}+3}+\dfrac{1}{\sqrt{x}-3}\right)\dfrac{4\sqrt{x}+12}{\sqrt{x}}\)
\(=\dfrac{\sqrt{x}-3+\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\dfrac{4\left(\sqrt{x}+3\right)}{\sqrt{x}}=\dfrac{2\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\dfrac{4\left(\sqrt{x}+3\right)}{\sqrt{x}}\)
\(=\dfrac{8}{\sqrt{x}-3}\)
b) \(A>B\Rightarrow-\sqrt{7}>\dfrac{8}{\sqrt{x}-3}\Rightarrow\dfrac{8}{\sqrt{x}-3}+\sqrt{7}< 0\)
\(\Rightarrow\dfrac{\sqrt{7x}+8-3\sqrt{7}}{\sqrt{x}-3}< 0\)
Ta có: \(\left\{{}\begin{matrix}8=\sqrt{64}\\3\sqrt{7}=\sqrt{63}\end{matrix}\right.\Rightarrow8-3\sqrt{7}>0\Rightarrow8-3\sqrt{7}+\sqrt{7x}>0\)
\(\Rightarrow\sqrt{x}-3< 0\Rightarrow\sqrt{x}< 3\Rightarrow x< 9\Rightarrow0< x< 9\)
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tính1.sqrt{147}+sqrt{54}-4sqrt{27}2.sqrt{28}-4sqrt{63}+7sqrt{112}3.sqrt{49}-5sqrt{28}+dfrac{1}{2}sqrt{63}4.left(2sqrt{6}-4sqrt{3}-dfrac{1}{4}sqrt{8}right).3sqrt{6}5.(2sqrt{1dfrac{9}{16}}-5sqrt{5dfrac{1}{16}}):sqrt{16}6.left(sqrt{48}-3sqrt{27}-sqrt{147}right):sqrt{3}7.left(sqrt{50}-3sqrt{49}right):sqrt{2}-sqrt{162}:sqrt{2}8.left(2sqrt{1dfrac{9}{10}}-sqrt{5dfrac{1}{10}}right):sqrt{10}9.2sqrt{dfrac{16}{3}}-3sqrt{dfrac{1}{27}}-6sqrt{dfrac{4}{75}}10.2sqrt{27}-6sqrt{dfrac{4}{3}}+dfrac{3}{5}sqrt{75}11....
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tính
1.\(\sqrt{147}+\sqrt{54}-4\sqrt{27}\)
2.\(\sqrt{28}-4\sqrt{63}+7\sqrt{112}\)
3.\(\sqrt{49}-5\sqrt{28}+\dfrac{1}{2}\sqrt{63}\)
4.\(\left(2\sqrt{6}-4\sqrt{3}-\dfrac{1}{4}\sqrt{8}\right).3\sqrt{6}\)
5.(\(2\sqrt{1\dfrac{9}{16}}-5\sqrt{5\dfrac{1}{16}}\)):\(\sqrt{16}\)
6.\(\left(\sqrt{48}-3\sqrt{27}-\sqrt{147}\right):\sqrt{3}\)
7.\(\left(\sqrt{50}-3\sqrt{49}\right):\sqrt{2}-\sqrt{162}:\sqrt{2}\)
8.\(\left(2\sqrt{1\dfrac{9}{10}}-\sqrt{5\dfrac{1}{10}}\right):\sqrt{10}\)
9.\(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
10.\(2\sqrt{27}-6\sqrt{\dfrac{4}{3}}+\dfrac{3}{5}\sqrt{75}\)
11.\(\dfrac{\sqrt{18}}{\sqrt{2}}-\dfrac{\sqrt{12}}{\sqrt{3}}\)
12.\(\dfrac{\sqrt{27}}{\sqrt{3}}+\dfrac{\sqrt{98}}{\sqrt{2}}-\sqrt{175}:\sqrt{7}\)
13.\(\left(\dfrac{\sqrt{8}}{\sqrt{2}}-\dfrac{\sqrt{180}}{\sqrt{5}}\right).\sqrt{5}-\sqrt{\dfrac{81}{11}}.\sqrt{11}\)
14.\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
15.\(\left(3\sqrt{2}-2\sqrt{3}\right)\left(3\sqrt{2}+2\sqrt{3}\right)\)
16.\(\left(1+\sqrt{5}-\sqrt{3}\right)\left(1+\sqrt{5}+\sqrt{3}\right)\)
So sánh:
a) \(-\dfrac{1}{3}\sqrt{63}và-2\sqrt{2}\)
b) \(-2\sqrt{55}và-\dfrac{3}{5}\sqrt{750}\)
c) \(-3\sqrt{7}và-\dfrac{1}{2}\sqrt{260}\)
a) \(\left(-\dfrac{1}{3}\sqrt{63}\right)^2=\dfrac{1}{9}\cdot63=7\)
\(\left(-2\sqrt{2}\right)^2=8\)
mà 7<8
nên \(-\dfrac{1}{3}\sqrt{63}>-2\sqrt{2}\)
b) Ta có: \(\left(2\sqrt{55}\right)^2=4\cdot55=220\)
\(\left(\dfrac{3}{5}\sqrt{750}\right)=\dfrac{9}{25}\cdot750=270\)
mà 220<270
nên \(2\sqrt{55}< \dfrac{3}{5}\sqrt{750}\)
hay \(-2\sqrt{55}< -\dfrac{3}{5}\sqrt{750}\)
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Q = \(\dfrac{1}{2}+\dfrac{3}{4}+\dfrac{7}{8}+\dfrac{15}{16}+\dfrac{31}{32}+\dfrac{63}{64}+\dfrac{127}{128}-6\)
Q=\(\dfrac{1}{2}+\left(\dfrac{3}{4}+\dfrac{7}{8}\right)+\left(\dfrac{15}{16}+\dfrac{31}{32}\right)+\left(\dfrac{63}{64}+\dfrac{127}{128}\right)-6\)
Q=\(\dfrac{1}{2}+\dfrac{13}{8}+\dfrac{61}{32}+\dfrac{253}{128}\)\(-6\)
Q= \(\dfrac{64}{128}+\dfrac{208}{128}+\dfrac{244}{128}+\dfrac{253}{128}-6\)
Q= \(\dfrac{769}{128}-6\)
Q=\(\dfrac{769}{128}-\dfrac{768}{128}\)
Q= \(\dfrac{1}{128}\)
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Không dùng mtct, so sánhA) sqrt{65}+1 và sqrt{63}+1B)dfrac{1}{sqrt{8}}và dfrac{1}{sqrt{7}}C)sqrt{34,9} và 6D) 3sqrt{25,5} và 14E)2sqrt{26}+4 và 13F) sqrt{24}+sqrt{63+3}và 16G) dfrac{46-3sqrt{49}}{4}và sqrt{50}
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Không dùng mtct, so sánh
A) \(\sqrt{65}\)+1 và \(\sqrt{63}\)+1
B)\(\dfrac{1}{\sqrt{8}}\)và \(\dfrac{1}{\sqrt{7}}\)
C)\(\sqrt{34,9}\) và 6
D) \(3\sqrt{25,5}\) và 14
E)\(2\sqrt{26}\)+4 và 13
F) \(\sqrt{24}\)+\(\sqrt{63+3}\)và 16
G) \(\dfrac{46-3\sqrt{49}}{4}\)và \(\sqrt{50}\)
e: \(2\sqrt{26}>9\)
nên \(2\sqrt{26}+4>13\)
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\(\dfrac{2}{7}\)của \(\dfrac{63}{91}\)
2/7 của 63/91
=63/91. 2/7
=18/91
chú thích : / là phần nha
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\(2\sqrt{112}-\dfrac{7}{6}\sqrt{252}-5\sqrt{63+3\sqrt{28}}\)
\(=2.4\sqrt{7}-\dfrac{7}{6}.6\sqrt{7}-5.3\sqrt{7}+3.2\sqrt{7}\)
\(=8\sqrt{7}-7\sqrt{7}-15\sqrt{7}+6\sqrt{7}\)
\(=-8\sqrt{7}\)
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