Cho a, b là hai số dương thoả mãn \(a^2-b^2\ge0\). Chứng minh:

\(\sqrt{\dfrac{a+\sqrt{a^2-b}}{2}}+\sqrt{\dfrac{a-\sqrt{a^2-b}}{2}}=\sqrt{a+\sqrt{b}}\)

Tìm max của: \(\dfrac{\sqrt{x}}{x-2\sqrt{x}+9}\)

Tìm GTLN của: \(\dfrac{\sqrt{x}+1}{2\sqrt{x}+1}\)

Tìm min và max của: \(A=\sqrt{5x-x^2}+\sqrt{18+3x-x^2}\)

Cho: 

\(A=\left(\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\dfrac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}\right):\left(\dfrac{1}{a}-\dfrac{1}{b}\right)\)

Biết \(2\sqrt{a}-\sqrt{b}=4\sqrt{ab}\). Tìm min A

30. His success is _____.

A. surprise B. surprised C. surprising D. surprisingly

31. We should _____ this road for better use.

A. wide B. to widen C. width D. widen

32. He finally _____ in finding a new job.

A. success B. succeeded C. successful D. successive

33. There is a _____ between the North and the South.

A. different B. differ C. differently D. difference

34. The North can be characterized as _____, cooler, hillier.

A. more industry B. industrial C. more industrial D. more industrially

35. People in the North say they work much _____ and speak more directly and honestly.

A. more hard B. more hardly C. more harder D. harder

36. This park is very _____ to visitors.

A. attract B. attraction C. attractive D. attracted

37. Here, in fine weather, can be seen hundreds of _____ people who have escaped for while from the noise and bustle of the town.

A. luck B. unlucky C. lucky D. luckily

38. In the world today, there are 5000 to 6000 living languages, of which English is by far the _____ used.

A. widely B. most widely C. most wide D. widest

39. He went to work as a driver on the Italian front where he was _____ wounded.

A. bad B. badly C. worse D. badder

40. I liked the T- shirt _____ he was wearing.

A. what B. which C. who D. whose