48 whispered

46. find

47. horible

48. ưhispered

49. followed

50. full 

1. D

2. B

3. A

4. C

5. C

6. D

7. A

8. B

9. A

10. D

II.

1. My sister managed to finish her work thoug she was ill

2. The test was difficult; however, the student did it well

3. She broke the vase I like best because she was careless

4. People use energy-saving bulbs in order to save electricity

5. We got on the wrong bus, so we were late for class

6. I get access to the Internet so that I can communicate with my friends

7. I enjoy watching dangerous sports and game shows

8. We should do more grammar exercises so as to improve our English

9. Because the red traffic lights isn't realized by him, he didn't stop

10. People are getting weaker and weaker since the air is more and more polluted 

12. D

13. A

14. B

15. A

16. D

17. C

18. A

19. B

20. C

a. Ta có \(\left(x+y\right)\left(x^2-xy+y^2\right)=x^3-x^2y+xy^2+x^2y-xy^2+y^3=x^3+y^3\)

\(\Rightarrow\left(x+y\right)\left(x^2-xy+y^2\right)=x^3+y^3\)

b. Ta có \(x^3+3x^2y+3xy^2+y^3=x^3+y^3+3xy\left(x+y\right)=\left(x+y\right)\left(x^2-xy+y^2\right)+3xy\left(x+y\right)=\left(x+y\right)\left(x^2+2xy+y^2\right)=\left(x+y\right)\left(x+y\right)^2=\left(x+y\right)^3\)\(\Rightarrow\left(x+y\right)^3=x^3+3x^2y+3xy^2+y^3\)

b. \(\left(4x^2-9\right)=0\)

\(\Leftrightarrow\left(2x-3\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\2x+3=0\end{matrix}\right.\) \(\Leftrightarrow x=\pm\dfrac{3}{2}\)

c. \(x^2+6x+9=0\)

\(\Leftrightarrow\left(x+3\right)^2=0\)

\(\Leftrightarrow x+3=0\)

\(\Leftrightarrow x=-3\)

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

\(\Leftrightarrow\left(x-3\right)\left(x-1-x+3\right)=0\)

\(\Leftrightarrow2\left(x-3\right)=0\)

\(\Leftrightarrow x-3=0\)

\(\Leftrightarrow x=3\)

a) \(f\left(0\right)=\dfrac{2}{7}.0-8=-8\)

\(f\left(2\right)=\dfrac{3}{7}.2-8=-\dfrac{50}{7}\)

\(f\left(-1\right)=\dfrac{3}{7}.\left(-1\right)-8=-\dfrac{59}{7}\)

\(f\left(-2\right)=\dfrac{3}{7}.\left(-2\right)-8=-\dfrac{62}{7}\)

b) Với mọi \(x_1,x_2\in R\), ta có

\(x_1>x_2\Leftrightarrow\dfrac{3}{7}x_1>\dfrac{3}{7}x_2\Leftrightarrow\dfrac{3}{7}x_1-8>\dfrac{3}{7}x_2-8\Leftrightarrow f\left(x_1\right)>f\left(x_2\right)\)

\(\Rightarrow\) Hàm số luôn đồng biến trên R

\(4x^2-4x-3=0\)

\(\Leftrightarrow\left(2x-1\right)^2-4=0\)

\(\Leftrightarrow\left(2x-1-2\right)\left(2x-1+2\right)=0\)

\(\Leftrightarrow\left(2x-3\right)\left(2x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\2x+1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)