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\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\\ =\sqrt{\left(\sqrt{3}\right)^2+2\cdot\sqrt{3}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{3}\right)^2-2\cdot\sqrt{3}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}\\ =\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\\ =\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}\\ =2\sqrt{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 3:
\(a)\left(x+2\right)\left(x+3\right)-\left(x-2\right)\left(x+5\right)=0\\ \Leftrightarrow x^2+3x+2x+6-\left(x^2+5x-2x-10\right)=0\\ \Leftrightarrow x^2+5x+6-x^2-3x+10=0\\ \Leftrightarrow2x+16=0\\ \Leftrightarrow2x=-16\\ \Leftrightarrow x=-\dfrac{16}{2}=-8\\ b)\left(x-3\right)\left(x-2\right)-\left(x+1\right)\left(x-5\right)=0\\ \Leftrightarrow\left(x^2-2x-3x+6\right)-\left(x^2-5x+x-5\right)=0\\ \Leftrightarrow x^2-5x+6-x^2+4x+5=0\\ \Leftrightarrow-x+11=0\\ \Leftrightarrow x=11\\ c)x\left(2x-5\right)-2x\left(x-6\right)=42\\ \Leftrightarrow2x^2-5x-2x^2+12x=42\\ \Leftrightarrow7x=42\\ \Leftrightarrow x=\dfrac{42}{7}\\ \Leftrightarrow x=6\\ d)\left(x-1\right)\left(2x+3\right)-2x\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(2x+3-2x\right)=0\\ \Leftrightarrow3\left(x-1\right)=0\\ \Leftrightarrow x-1=0\\ \Leftrightarrow x=1\)
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Bài 1:
a) Để căn thức có nghĩa thì:
\(x+1\ge0\Leftrightarrow x\ge-1\)
b) Để căn thức có nghĩa thì:
\(3x-8\ge0\Leftrightarrow3x\ge8\Leftrightarrow x\ge\dfrac{8}{3}\)
c) Để căn thức có nghĩa thì:
\(2x^2+3>0\)
Mà điều này luôn đúng nên căn thức có nghĩa khi x ∈ R
d) Để căn thức có nghĩa thì:
\(16-x^2\ge0\Leftrightarrow\left(4-x\right)\left(4+x\right)\ge0\Leftrightarrow-4\le x\le4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Ta có DE vuông AB
AH vuông AB
=> DE // AH
b, Ta có DE // AH => ^BDE = ^ACB ( 2 góc đồng vị )
=> ^BDE = ^DCH = 400
c, Ta có DH vuông AC
AB vuông AC
=> DH // AB
Ta có DH // AB; ED//AH ; ^EAH = ^AED = ^AHD = 900
Vậy tứ giác AEDH là hình vuông
=> DE vuông DH
![](https://rs.olm.vn/images/avt/0.png?1311)
Số xe cửa hàng nhập về là:
\(80:32\%=250\) (chiếc)
Số xe cửa hàng còn lại là:
`250 - 80 =170` (chiếc)
ĐS: ...
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Bài 1
1 am working
2 doesn't rain
3 are you looking
4 is getting
5 am going
![](https://rs.olm.vn/images/avt/0.png?1311)
1 We are often taken to the zoo by our father at weekends
2 Hundreds of pupils wre greeted by the smell of fresh paint
3 Noise shouldn't be made by you
4 How can our fields be kept in good condition?
5 Was Lan given an English-Vietnamese dictionary by you?
6 By whom was "Gulliver's travels" written?
7 Why were these books bought?
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\(\dfrac{4}{\sqrt{5}+\sqrt{3}}-\sqrt{20}\\ =\dfrac{4\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}-\sqrt{20}\\ =\dfrac{4\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}\right)^2-\left(\sqrt{3}\right)^2}-\sqrt{2^2\cdot5}\\ =\dfrac{4\left(\sqrt{5}-\sqrt{3}\right)}{5-3}-2\sqrt{5}\\ =\dfrac{4\left(\sqrt{5}-\sqrt{3}\right)}{2}-2\sqrt{5}\\ =2\left(\sqrt{5}-\sqrt{3}\right)-2\sqrt{5}\\ =2\sqrt{5}-2\sqrt{3}-2\sqrt{5}\\ =-2\sqrt{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left|x+\dfrac{1}{1\cdot3}\right|+\left|x+\dfrac{1}{3\cdot5}\right|+...+\left|x+\dfrac{1}{197\cdot199}\right|=100x\)
Số lượng số hạng là: \(\left(199-3\right):2+1=99\) (số hạng)
TH1: \(x\ge-\dfrac{1}{197\cdot199}\)
\(=>\left(x+\dfrac{1}{1\cdot3}\right)+\left(x+\dfrac{1}{3\cdot5}\right)+...+\left(x+\dfrac{1}{197\cdot199}\right)=100x\\ =>\left(x+x+...+x\right)+\left(\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{197\cdot199}\right)\\ =>99x+\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{197\cdot199}\right)\\ =>100x-99x=\dfrac{1}{2}\cdot\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{197}-\dfrac{1}{199}\right)\\ =>x=\dfrac{1}{2}\cdot\left(1-\dfrac{1}{199}\right)=\dfrac{1}{2}\cdot\dfrac{198}{199}\\ =>x=\dfrac{99}{199}\left(tm\right)\)
TH2: \(x\le-\dfrac{1}{1\cdot3}\)
\(=>-\left(x+\dfrac{1}{1\cdot3}\right)-\left(x+\dfrac{1}{3\cdot5}\right)-...-\left(x+\dfrac{1}{197\cdot199}\right)=100x\\ =>-\left[\left(x+x+...+x\right)+\left(\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{197\cdot199}\right)\right]=100x\\ =>-\left[99x+\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{197\cdot199}\right)\right]=100\\ =>-99x-\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{197}-\dfrac{1}{199}\right)=100x\\ =>100x+99x=-\dfrac{1}{2}\left(1-\dfrac{1}{199}\right)\\ =>199x=-\dfrac{1}{2}\cdot\dfrac{198}{199}\\ =>199x=-\dfrac{99}{199}\\ =>x=-\dfrac{99}{199}:199=-\dfrac{99}{39061}\left(ktm\right)\)
Vậy: `x=99/199`
\(a)2^3-50:25+13\cdot7=8-2+91\\ =6+91\\ =97\\ b)60-\left[120-\left(42-33\right)\cdot2\right]\\ =60-\left(120-9\cdot2\right)\\ =60-\left(120-18\right)\\ =60-102\\ =-42\\ c)3^{17}:3^{15}+8\cdot3\\ =3^{17-15}+24\\ =3^2+24\\ =9+24\\ =33\\ d)12:\left\{390:\left[500-\left(125+35\cdot7\right)\right]\right\}\\ =12:\left\{390:\left[500-\left(125+245\right)\right]\right\}\\ =12:\left[390:\left(500-370\right)\right]\\ =12:\left(390:130\right)\\ =12:3=4\)