1)2x(25x-4)-(5x-2)(5x+1)=8 / 5)\(2\left(x-2\right)-3\left(3x-1\right)=\left(x-3\right)\)

2)x(4x-3)-(2x-2)(2x-1)=5 / 6)\(\frac{2}{x+1}-\frac{1}{x-2}=\frac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

3)\(\frac{5}{2x+3}+\frac{3}{9-x^2}=\frac{8}{7\left(x=3\right)}\) / 7)\(\frac{5x-2}{6}+\frac{3-4x}{2}=2-\frac{x+7}{3}\)

4)\(\frac{2}{3\left(x-2\right)}+\frac{5}{12-3x^2}=\frac{3}{4\left(x+2\right)}\) / 8)\(\frac{2}{x+1}-\frac{1}{x-2}=\frac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

câu 1 : Giải pt sau 
a . \(2x-2\sqrt{2x}-1=0\)

câu 2 : thu gọn các biểu thức sau 

\(A=\frac{3+\sqrt{5}}{3-\sqrt{5}}+\frac{3-\sqrt{5}}{3+\sqrt{5}}\)
\(B=\sqrt{12-6\sqrt{3}}+\sqrt{21-12\sqrt{3}}\)

\(C=5\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}-\sqrt{\frac{5}{2}}\right)^2+\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}-\sqrt{\frac{3}{x}}\right)^2\) 
 

Tìm x biết :

4,\(\frac{\left(-3\right)^x}{81}=-27\)

5,\(1\frac{1}{2}.x-4=0,5\)

6,\(2^{x-1}=16\)

7,\(\left(x-1\right)^2=25\)

8,\(|2x-1|=5\)

9,\(0,2-|4,2-2x|=0\)

11,\(1\frac{2}{3}:\frac{x}{4}=6:0,3\)

12,\(2\frac{2}{3}:x=1\frac{7}{9}:2\frac{2}{3}\)

Bài 1: Tính

\(\dfrac{1}{4}+\dfrac{5}{10}-\dfrac{1}{3}-\dfrac{7}{8}\)

Bài 2:Tính bằng cách hợp lí

a) A= \(11\dfrac{3}{13}-\left(2\dfrac{4}{7}+5\dfrac{3}{13}\right)\)

b) B= \(\left(6\dfrac{4}{9}+3\dfrac{7}{11}\right)-4\dfrac{4}{9}\)

c) C= \(\dfrac{-5}{7}.\:\dfrac{2}{11}+\dfrac{-5}{7}.\dfrac{9}{11}+1\dfrac{5}{7}\)

d) D= \(0,7.\:2\dfrac{2}{3}.20.\:0,375.\:\dfrac{5}{28}\)

e) E= \(\left(-6,17+3\dfrac{5}{9}-2\dfrac{36}{97}\right).\left(\dfrac{1}{3}-0,25-\dfrac{1}{12}\right)\)

Bài 5: Tính nhanh

A=\(25.20,04+4.20,04-2004.20,33+2004.20,04\)

Bài 6: So sánh

\(\dfrac{10^5+4}{10^5-1}\)và \(\dfrac{10^5+3}{10^5-2}\)

1. \(x^3-x^2+12x\sqrt{x-1}+20=0\)

2. \(x^3+\sqrt{\left(x-1\right)^3}=9x+8\)

3. \(\sqrt{2x^2+x+1}+\sqrt{x^2-x+1}=3x\)

4. \(x^6+\left(x^3-3\right)^3=3x^5-9x^2-1\)

5. \(x^2-6\left(x+3\right)\sqrt{x+1}+14x+3\sqrt{x+1}+13=0\)

6. \(x^2-4x+\left(x-3\right)\sqrt{x^2-x+1}=-1\)

7. \(\sqrt{2x-1}+\sqrt{5-x}=x-2+2\sqrt{-2x^2+11x-5}\)

8. \(\sqrt{5x+11}-\sqrt{6-x}+5x^2-14x-60=0\)

9. \(x^2+6x+8=3\sqrt{x+2}\)

10. \(2x^2+3x-2=\left(2x-1\right)\sqrt{2x^2+x-3}\)

11. \(\sqrt{x+1}+\sqrt{4-x}-\sqrt{\left(x+1\right)\left(4-x\right)}=1\)

12. \(x^2-\sqrt{x^2-4x}=4\left(x+3\right)\)

13. \(x^2-x-4=2\sqrt{x-1}\left(1-x\right)\)

14. \(\frac{1}{\sqrt{x}+1}+\frac{1}{\sqrt{x}-1}=1\)

15. \(\sqrt{2x^2+3x+2}+\sqrt{4x^2+6x+21}=11\)

16. \(\sqrt{x+3+3\sqrt{2x-3}}+\sqrt{x-1+\sqrt{2x-1}}=2\sqrt{2}\)

17. \(\left(x-2\right)^2\left(x-1\right)\left(x-3\right)=12\)

18. \(2x^2+\sqrt{x^2-2x-19}=4x+74\)

19. \(x^4+x^2-20=0\)

20. \(x+\sqrt{4-x^2}=2+3x\sqrt{4-x^2}\)

21. \(\left(x^2+x+1\right)\left(\sqrt[3]{\left(3x-2\right)^2}+\sqrt[3]{3x-2}+1\right)=9\)

22. \(\sqrt{x^2-3x+5}+x^2=3x+7\)

23. \(x^2+6x+5=\sqrt{x+7}\)

24. \(\frac{2x^2-3x+10}{x+2}=3\sqrt{\frac{x^2-2x+4}{x+2}}\)

25. \(5\sqrt{x-1}-\sqrt{x+7}=3x-4\)

26. \(2\left(x^2+2\right)=5\sqrt{x^3+1}\)

27. \(\sqrt{x-1}+\sqrt{5-x}-2=2\sqrt{\left(x-1\right)\left(5-x\right)}\)

28. \(x^2+\frac{9x^2}{\left(x-3\right)^2}=40\)

29. \(\frac{26x+5}{\sqrt{x^2+30}}+2\sqrt{26x+5}=3\sqrt{x^2+30}\)

30. \(\frac{\sqrt{27+x^2+x}}{2+\sqrt{5-\left(x^2+x\right)}}=\frac{\sqrt{27+2x}}{2+\sqrt{5-2x}}\)

Giai pt

1,\(\sqrt{x+8-6\sqrt{x-1}}\)=4

2,\(\sqrt{x+6-2\sqrt{x+2}}\)+\(\sqrt{x+11-6\sqrt{x+2}}\)=1

3,\(\sqrt{x-3-2\sqrt{x-4}}\)+\(\sqrt{x-4\sqrt{x-4}}\)=1

4,\(\sqrt{x-2+\sqrt{2x+5}}\)+\(\sqrt{x+2+3\sqrt{2x-5}}\)=\(\dfrac{7}{2}\)

5,\(\sqrt{2x+4+6\sqrt{2x-5}}\)+\(\sqrt{2x-4-2\sqrt{2x-5}}\)=4

6,\(\sqrt{\dfrac{1}{4}x^2+x+1}\)-\(\sqrt{6-2\sqrt{5}}\)=0

7,x+\(\sqrt{x+\dfrac{1}{2}}\)+\(\sqrt{x+\dfrac{1}{4}}\)=2

8,\(\sqrt{\left(x-1\right)+4-4\sqrt{x-1}}+\sqrt{x-1-6\sqrt{x-1+9}}\)=1

9,\(\sqrt{x+2\sqrt{x-1}}\)+\(\sqrt{x-2\sqrt{x-1}}\)=\(\dfrac{x+3}{2}\)

Bài 3 : giải các bất phương trình sau

21 , \(\frac{2}{x-1}\le\frac{5}{2x-1}\)

22, \(\frac{-4}{3x+1}< \frac{3}{2-x}\)

23 , \(\frac{2x^2+x}{1-2x}\ge1-x\)

24 , \(\frac{2x-5}{3x+2}< \frac{3x+2}{2x-5}\)

25 , \(2x^2-5x+2< 0\)

26 , \(-5x^2+4x+12< 0\)

27 , \(16x^2+40x+25>0\)

28 , \(-2x^2+3x-7\ge0\)

29 , \(3x^2-4x+4\ge0\)

30 , \(x^2-x-6\le0\)

2. Tìm các tính chất đặc trưng của các phần tử thuộc tập hợp:

\(C=\left\{\text{2, 3, 5, 7, 11, 13}\right\}\)

\(D=\left\{1-\sqrt{3},1+\sqrt{3}\right\}\)

\(E=\left\{\text{1, 2, 5, 10, 17,26, 37}\right\}\)

\(F=\left\{\frac{1}{2},\frac{1}{6},\frac{1}{12},\frac{1}{20},\frac{1}{30}\right\}\)

\(G=\left\{\frac{2}{3},\frac{3}{8},\frac{4}{15},\frac{5}{24},\frac{6}{35}\right\}\)

1)(x+4).(x+1)-3\(\sqrt{x^2+5x+2}\)=6

2)(\(^{x^2}\)+5x+4)\(\sqrt{x+3}\)=0

3)\(\left\{{}\begin{matrix}x-y=1\\x^2-xy+y^2=7\end{matrix}\right.\)

4)(x+1)\(\sqrt{x^2-2x+3}\)=\(^{x^2}\)+1

5)\(\left|4x+7\right|\)-2x-5=0

6)\(\sqrt{5x-1}\)=\(\sqrt{x}\)+4x-1

7)\(\sqrt{x^2+x-12}\)=8-x

8)\(\sqrt{x^2+2x+4}\)=\(\sqrt{2-x}\)