KHI VIẾT THÊM CHỮ 7 VÀO SỐ 3267 THÌ ĐƯỢC ĐƯỢC SỐ MỚI HƠN SỐ CŨ BAO NHIÊU ĐƠN VỊ ?
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Câu 1 :
a, \(A=\left(\frac{1}{\sqrt{a}-1}+\frac{1}{\sqrt{a}+1}\right).\frac{1}{\sqrt{a}}\)
\(=\left(\frac{\sqrt{a}+1}{a-1}+\frac{\sqrt{a}-1}{a-1}\right).\frac{1}{\sqrt{a}}=\frac{2\sqrt{a}}{a-1}.\frac{1}{\sqrt{a}}=\frac{2}{a-1}\)
b, Ta có :A = 1 hay \(\frac{2}{a-1}=1\Leftrightarrow a-1=2\Leftrightarrow a=3\)( tmđkxđ )
Câu 3 :
\(\hept{\begin{cases}2x-3y=1\left(1\right)\\3x+y=7\left(2\right)\end{cases}}\)Ta có : \(y=7-3x\)(k)
Thay vào phương trình 1 ta được :
\(2x-3\left(7-3x\right)=1\)
\(\Leftrightarrow2x-21+9x=1\Leftrightarrow11x=22\Leftrightarrow x=2\)
Thay vào (k) ta được : \(y=7-3.2=7-6=1\)
Vậy \(\left\{x;y\right\}=\left\{2;1\right\}\)

Kẻ \(AH\perp DC\) , \(BK\perp DC\)
Xét tứ giác ABKH có: AB // HK (gt)
AH // BK ( cùng \(\perp DC\))
=> ABKH là hình chữ nhật (dhnb)
=> HK = AB = 4, AH = BK
Xét △ ADH vuông tại H và △BCK vuông tại K
Có: AH = BK (cmt)
AD = BC (ABCD là hình thang cân)
=> △ADH = △BCK (ch-cgv)
=> DH = KC
Ta có: DH + HK + KC = DC
=> 2DH + HK = 10
=> 2DH + 4 = 10
=> 2DH = 6
=> DH = 3 = CK
Ta có: DK = DH + HK = 3 + 4 = 7
Xét △DEF vuông tại F có: BF là đường trung tuyến
=> BF = BD = DE/2
=> △BFD cân tại B
mà BK là đường cao ( \(BK\perp DF\))
=> BK là đường trung tuyến
=> DK = KF = 7
Ta có: CF = KF - KC = 7 - 3 = 4
b) Chắc đề bài bạn gõ sai, phải là \(AM.BN=\frac{AB^2}{4}\).
Gọi giao giữa tiếp tuyến \(MN\)và \(\left(O\right)\)là \(H\).
Tam giác \(MON\)vuông tại \(O\), đường cao \(OH\)nên có:
\(MH.NH=OH^2\)
mà \(MA=MH,NB=NH\)(tính chất 2 tiếp tuyến giao nhau) , \(AB=2R\)suy ra
\(AM.BN=MH.NH=OH^2=R^2=\frac{AB^2}{4}\)
Exercise 3: Choose the best one (A, B, C or D) to complete the sentence.
1. They repaired the furniture in our village school and also _______the houses for elderly people.
A. fixed B. removed C. renewed D. regenerated
2. Care _________ the young and the old is a public responsibility.
A. with B. for C. to D. about
3. They had found ways to ________funds to support their activities.
A. rise B. collect C. gather D. raise
4. They ________ a lot of flowers in their garden and around their house.
A. place B. plant C. put D. pick down
5. She has only to ________ the meals, look after the children, and keep the house in order.
A. take B. cook C. do D. make
6. Girls may also be made to do chores when they could be learning, and not be allowed to take ______ sports.
A. part in B. one in C. into D. take for
7. They want prosperity but they also want a ______ environment, good health, social protection.
A. cleaning B. cleaned C. clean D. cleanness
8. He ______ thousands of pounds to charity.
A. put B. donated C. transmitted D. took
9. At Tet, my mother and her close friends often go to the hospitals to donate cakes, sweets and toys for the sick children there. She _________ it for many years.
A. is doing B. have done C. has done D. did
10. The volunteers have raised funds to _________ homeless people.
A. bring B. help C. rescue D. bear
11. The last aim is to _______ fresh drinking water at the lowest cost possible.
A. do B. make C. provide D. give
12. Mr. Brown and some ________ are on a very dirty beach now to ________ the beach a clean and beautiful place again.
A. volunteers - make B. volunteering - get C. voluntary - do D. volunteer - change
13. It is very positive for children to study hard if they’re ________ to do so.
A. exciting B. interesting C. eager D. bored
14. Vietnamese people have had the __________of helping one another since the early days of the country.
A. custom B. legend C. tradition D. religion
15. A volunteer always helps other people willingly and ____ payment.
A. for B. within C. about D. without
16. They save people money as well as having health ________.
A. benefits B. forces C. problems D. events
17. They volunteer by ______ children from poor families in their community.
A. talking B. singing C. encouraging D. tutoring
18. All the members have to collect glass, waste paper and empty cans and send them for _____.
A. recycling B. reusing C. producing D. reselling
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