CM CĐTS:

1)(\(\dfrac{\sqrt{14}-\sqrt{7}}{2\sqrt{2}-2}+\dfrac{\sqrt{15}-\sqrt{5}}{2\sqrt{3}-2}\)):\(\dfrac{1}{\sqrt{7}-\sqrt{5}}=1\)

<=>[\(\dfrac{\sqrt{7}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}+\dfrac{\sqrt{5}\left(\sqrt{3}-1\right)}{2\left(\sqrt{3}-1\right)}\)]:\(\dfrac{1}{\sqrt{7}-\sqrt{5}}=1\)

<=>\(\left(\dfrac{\sqrt{7}}{2}+\dfrac{\sqrt{5}}{2}\right).\left(\sqrt{7}-\sqrt{5}\right)=1\)

<=>\(\dfrac{\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)}{2}=1\)

<=>\(7-5=2\)

<=>2=2(luôn đúng)

2)\(\dfrac{4}{3+\sqrt{5}}+\dfrac{8}{\sqrt{5}-1}-\sqrt{\left(2-\sqrt{5}\right)^2}=7\)

<=>\(\dfrac{8}{6+2\sqrt{5}}+\dfrac{8}{\sqrt{5}-1}+\left(2-\sqrt{5}\right)=7\)

<=>\(\dfrac{8}{\left(\sqrt{5}+1\right)^2}+\dfrac{8}{\left(\sqrt{5}-1\right)}+2-\sqrt{5}=7\)

<=>\(\dfrac{8\left(\sqrt{5}-1\right)+8\left(\sqrt{5}+1\right)^2}{\left(\sqrt{5}+1\right)^2\left(\sqrt{5}-1\right)}+2-\sqrt{5}=7\)

<=>\(\dfrac{40+24\sqrt{5}}{4\left(\sqrt{5}+1\right)}+2-\sqrt{5}=7\)

<=>\(\dfrac{4\left(10+6\sqrt{5}\right)}{4\left(\sqrt{5}+1\right)}-\sqrt{5}=5\)

<=>\(\dfrac{10+6\sqrt{5}}{\sqrt{5}+1}-\sqrt{5}=5\)

<=>\(\dfrac{10+6\sqrt{5}-5-\sqrt{5}}{\sqrt{5}+1}=5\)

<=>\(\dfrac{5+5\sqrt{5}}{\sqrt{5}+1}=5\)

<=>\(5=5\)(đúng)

l

1)

<=> A=\(\sqrt{3+2\sqrt{3}+1}-\sqrt{4+2.2.\sqrt{3}+3}\)

<=>\(A=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(2+\sqrt{3}\right)^2}\)

<=>\(A=\left|\sqrt{3}+1\right|-\left|2+\sqrt{3}\right|\)

<=>\(A=\sqrt{3}+1-2-\sqrt{3}\)

<=>\(A=-1\)

B=\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)

<=>\(B=\sqrt{3+2.\sqrt{3}.\sqrt{2}+2}-\sqrt{3-2.\sqrt{3}.\sqrt{2}+2}\)

<=>\(B=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)

<=>\(B=\sqrt{3}+\sqrt{2}-\left(\sqrt{3}-\sqrt{2}\right)\)

<=>\(B=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}\)

<=>\(B=2\sqrt{2}\)

C=\(\sqrt{x+2-2\sqrt{x+1}}+\sqrt{x+2+2\sqrt{x+1}}\)

ĐK: \(x+1\ge0\Leftrightarrow x\ge-1\)

\(\Leftrightarrow C=\sqrt{\left(x+1\right)-2\sqrt{x+1}+1}+\sqrt{\left(x+1\right)+2\sqrt{x+1}+1}\)\(\Leftrightarrow C=\sqrt{\left(\sqrt{x+1}-1\right)^2}+\sqrt{\left(\sqrt{x+1}+1\right)^2}\)

\(\Leftrightarrow C=\left|\sqrt{x+1}-1\right|+\left|\sqrt{x+1}+1\right|\)

TH₁: \(-1\le x< 0\)

\(\Leftrightarrow C=-\sqrt{x+1}+1+\sqrt{x+1}+1\)

\(\Leftrightarrow C=2\)

TH₂:\(x\ge0\)

\(\Leftrightarrow C=\sqrt{x+1}-1+\sqrt{x+1}+1\)

\(\Leftrightarrow C=2\sqrt{x+1}\)

Vậy khi \(-1\le x< 0\)thì\(\Leftrightarrow C=2\)

KHi \(x\ge0\)thì \(\Leftrightarrow C=2\sqrt{x+1}\)

Exercise 1. Put the verb into the most suitable form, past perfect or past perfect continuous

1. I…................................... (wait) for hours, so I was really glad when the bus finally ...................(arrive).

2. Why….........................(be) the baby’s face so dirty? He….............. (eat) chocolate.

3. I …......................(see) John yesterday, but he ….................(run). So he was too tired to chat.

4. It ….......................(rain) and the pavement …...............(be) covered with puddles.

5. When I …...........(arrive), it was clear that she…................................. (work). There were papers all over the floor and books everywhere.

6. They ….....................(study) all day so, when we….............. (meet), they were exhausted.

7. The boss …...................(talk) to clients on Skype for hours, so she….................(want) a break.

8. Peter was Sally’s best friend. She…..................(know) him all her life.

9. The children were wet because they….............(play) football in the rain.

10. We were very hungry because we…..................(not / eat).

11. I was delighted when I found my keys. I…...........(look) for them for hours.

12. She was exhausted because she…........(work) since eight o’clock that morning.

13. Everything was white because it….......................(snow).

14. The passengers were cross because the airline….............(lose) everyone’s bags.

15. I…...................(not / see) Jacob for several years, but I ecognized him immediately.

1. It was very noisy next door. Our neighbours …………….(have) a party.

2. We were good friends. We……………..(know) each other for years.

3. John and I went for a walk. I had difficulty keeping up with him because he………….(walk) so fast.

4. Sue was sitting on the ground. She was out of breath. She……………….(run).

5. When I arrived, everybody was sitting round the table with their mouths full. They……………………………(eat).

6. When I arrived, everybody was sitting round the table and talking. Their mouths were empty but their stomachs were full. They…………………………..(eat).

7. Jim was on his hands and knees on the floor. He …………….(look) for his contact lens.

8. When I arrived, Kate……………………….(wait) for me. She was annoyed with me because I was late and she…………….(wait) for a long time.

9. I was sad when I sold my car. I……………….(have) it for a very long time.

10. We were extremely tired at the end of the journey. We……………………..(travel) for more than 24 hours.

Bài về nhà

Exercise 1. Put the verb into the correct form, will be (do)ing or will have (done).

1. Don't phone between 7 and 8. We............................. (we / have) dinner then.

2. Phone me after 8 o'clock. .......................... (we / finish) dinner by then.

3. Tomorrow afternoon we're going to play tennis from 3 o'clock until 4.30. So at 4 o'clock,.........................................(we / play) tennis.

4. A: Can we meet tomorrow?

B: Yes, but not in the afternoon............................................. (I / work).

5. B has to go to meeting which begins at 10 o'clock. It will last about an hour.

A: Will you be free at 11.30?

B: Yes,..................... (the meeting / end) by then.

6 Ben is on holiday and he is spending his money very quickly. If he continues like this, .......................... (he / spend) all his money before the end of his holiday.

7 Do you think................................ (you / still / do) the same job in ten years' time?

8. Lisa is from New Zealand. She is travelling around Europe at the moment. So far she has travelled about 1,000 miles. By the end of the trip,.............................. (she / travel) more than 3,000 miles.

9 If you need to contact me,.....................(I /stay) at the Lion Hotel until Friday.

10 A:........................(you / see) Laura tomorrow?

B: Yes, probably. Why?

A: I borrowed this CD from her. Can you give it back to her?

11. At midnight we .......................... (sleep).

12. This time next week we ............................. (sit) at the beach.

13. At nine I ...................... (watch) the news.

14. Tonight we ..................... (cram up) for our English test.

Exercise 2: The Future Perfect & The Future Perfect Continuous

1) This spring, the twins (attend) culinary school for two years.

2) Danielle (not give) her speech by the time Andrew gives his

3) By the end of the year, our church’s attendance (increase) by at least 10 percent per year for the past 20 years.

4) How much rent the tenants (pay) by the end of the year?

5) When Mr. Ramirez retires, he (teach) _ for 34 years.

6) Brent (read) more books than Trish by the end of the summer

7) The harpist needs a break. After this piece, she (play) for two hours straight.

8) By 2012, will our city (recover) from the hurricane for ten years.

9) you (finish) your teaching when the semester ends?

10) This time tomorrow, Maria on a beach in Majorca. (sunbathe)

11) Wake me up by nine o'clock - I long enough by then. (sleep)

12) Look, I can give you a lift to the station - I that way anyway. (drive)

13) It's strange that when we get to Sydney, we half way round the world. (fly)

14) Don't phone me between 7 and 8. We dinner then. (have)

15) Phone me after 8 o'clock. We dinner by then. (finish)

16) Tomorrow afternoon we're going to play tennis from 3 o'clock until 4.30. So at 4 o'clock, we

tennis. (play)

17) Do you think you the same job in ten years' time? (still/do)

18) By the time you get home I the house from top to bottom. (clean)

19) Tom is on holiday and he is spending his money very quickly. If he continues like this, he all his money before the end of his holiday. (spend)

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