Cho a,b,c khác 0 thỏa mãn a\(\left(\dfrac{1}{c}+\dfrac{1}{b}\right)+b\left(\dfrac{1}{c}+\dfrac{1}{a}\right)+c\left(\dfrac{1}{a}+\dfrac{1}{b}\right)=-2\)
a(1b+1c)+b(1c+1a)+c(1a+1b)=−2
và a3+b3+c3=1. CMR \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1\)
Bài 1: Cho abcd=1. Tính P = aabc+ab+a+1+bbcd+bc+d+1+ccda+cd+a+1+ddab+da+b+1aabc+ab+a+1+bbcd+bc+d+1+ccda+cd+a+1+ddab+da+b+1
Bài 2: Cho a, b, c luôn dương và a3+b3+c3=3abca3+b3+c3=3abc. Tính Q = (1+ab)(1+bc)(1+ca)(1+ab)(1+bc)(1+ca)
Bài 3: Cho x2+y2+z2−zx+4y=6z−14x2+y2+z2−zx+4y=6z−14. Tính P = x1945+y2+zx1945+y2+z
Bài 4: Cho a+b+c=1
a^2+b^2+c^2=1
a^3+b^3+c^3=1
Tính a^2005+b^2006+c^2007
Bài 5: Cho 1a+1b+1c=51a+1b+1c=5 và a+b+c=abc. Tính 1a2+1b2+1c2
Cho a,b,c≠0a,b,c≠0 và a+b+c≠0a+b+c≠0 thỏa mãn điều kiện 1a+1b+1c=1a+b+c1a+1b+1c=1a+b+c.
Chứng minh rằng trong ba số a,b,c có hai số đối nhau. Từ đó suy ra rằng:
1a2009+1b2009+1c2009=1a2009+b2009+c2009
1/a + 1/b + 1/c = 1/a+b+c => \(\frac{ab+bc+ac}{abc}\)= \(\frac{1}{a+b+c}\)=> ( ab + bc + ac ) =abc => a2b +ab2 +bc2+b2c+ac2+a2c +3abc = abc
=> a2b+ab2+bc2+ac2+a2c+b2c+abc+abc=0 . Sau đó,bạn phân tích được là : (a+c)(b+c)(a+b)=0 => a=-c hoặc a=-b hoặc b=-c
Vậy trong ba số a,b,c có hai số đối nhau(đpcm).
Câu hỏi của Nguyễn Đa Vít - Toán lớp 9 - Học toán với OnlineMath
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Cho (a2−bc)(b−abc)=(b2−ac)(a−abc);abc≠0;a≠b(a2−bc)(b−abc)=(b2−ac)(a−abc);abc≠0;a≠b
CMR:1a+1b+1c=a+b+c
II. Find one odd word A, B, C or D. (1p)
1. A. terrifying B. thrilling C. fascinating D. delicious
2. A. fresh B. convincing C. believable D. interesting
3. A. excellent B. interesting C. amusing D. bad-tempered
4. A. fantastic B. wonderful C. brilliant D. lazy
5. A. dramatic B. funny C. beautiful D. boring
II. Find one odd word A, B, C or D. (1p)
1. A. terrifying B. thrilling C. fascinating D. delicious
2. A. fresh B. convincing C. believable D. interesting
3. A. excellent B. interesting C. amusing D. bad-tempered
4. A. fantastic B. wonderful C. brilliant D. lazy
5. A. dramatic B. funny C. beautiful D. boring
1. Find the word which has different sound in the part underlined. (1P)
1. A. matches B. parades C. decides D. relatives
2. A. clothing B. hold C. poster D. dove
3. A. comb B. climb C. suburb D. bomb
4. A. although B. think C. gather D. other
5. A. headline B. heating C. meal D. leave
I.Choose a word in each group that is pronounced differently from
others. (1p)
1. A. purpose B. survey C. turkey D. cultural
2. A. hour B. vehicle C. honest D.
helicopter
3. A. machine B. children C. challenge D. charity
4. A. pleased B. washed C. raised D. learned
5. A. lies B. gives C. matches D. temples
I.Choose a word in each group that is pronounced differently from
others. (1p)
1. A. purpose B. survey C. turkey D.cultural
2. A.hour B. vehicle C. honest D.helicopter
3.A. machine B. children C. challenge D. charity
4. A. pleased B. washed C. raised D.learned
5. A. lies B. gives C.matches D. temples
II. Odd one out. (1p)
1. A. wants B. needs C. goes D. likes
2. A. city B. building C. village D. countryside
3. A. house B. office C. classroom D. library
4. A. recycle B. relax C. reuse D. reduce nderlined part .
I.Choose the word whose main stress is placed differently from the others.(1P)
Câu 1: A. excited B. similar C. register D. citizen
Câu 2: A. sidewalk B. drawing C. support D. garden
Câu 3: A. tutor B. equipment C. hobby D. interest
Câu 4: A .academic B. application C. education D.behavior
II.Choose the word that has the underlined part pronounced differently from the others.(1P)
Câu 5: A. aim B. raise C. mainly D. certainly
Câu 6: A. classmate B. national C. application D. paper
- Where is underlined part ???
Câu 7: A. enroll B. program C. hobby D. over
Câu 8: A. unite B. used C. voluntary D. usua1ly
I/ Circle the word whose underlined part is pronounced differently from the others (1p)
A. solar B. power C. eco-friendly D. hydro
A. pedal B. invent C. expensive D. plentiful
II/ Circle the word which has a different stress pattern from the others (1p)
A. appear B. pilot C. pollute D. replace
A. abundant B. imagine C. solution D. driverless
III/ Choose the best option (3p)
I think perhaps we ______ flying cars soon.
A. will have B. will be having C. are going to have D. are having
Does that red motorbike belong to your mother? - No, ______ is white.
A. she B. her C. hers D. mine
We should try to make the world greener by using vehicles that are ______ .
A. environmental friendly B. environmentally friendly
C. friendly environment D. friendly environmental
Mai usually goes to school ______ bus but yesterday she came ______ her dad’s car.
A. in / on B. on / in C. by / in D. by / by
At this time next week, we ______ a wind turbine in our garden.
A. install B. have installed C. will install D. will be installing
Natural gas is a non-renewable source of energy and it may ______ soon.
A. run out B. run down C. use up D. use over
IV/ Give the correct form of the words in brackets (2p)
We couldn’t see the airplane because it _____________ behind the cloud. (appear)
Your idea is really _____________ , however, I don’t think it will come true soon. (imagine)
Vesak Day is a _____________ festival for those who follow Buddhism. (religion)
The traffic in some cities is so _____________ that it is difficult to see a solution. (chaos)
V/ Write questions for the underlined parts (1.5p)
The highlight of the festival is the tomato fight.
The Songkran Festival is usually celebrated between 13 and 16 of April.
It costs about $500 to join Glastonbury Festival.
VI/ Rewrite the following sentences, beginning with the given words (1.5p)
We will plant more trees to reduce the carbon dioxide.
More trees
I hope they will choose John for the school’s football team.
I hope John
The local government will build a power station here next year.
A power station
I/ Circle the word whose underlined part is pronounced differently from the others (1p)
A. solar B. power C. eco-friendly D. hydro
A. pedal B. invent C. expensive D. plentiful
II/ Circle the word which has a different stress pattern from the others (1p)
A. appear B. pilot C. pollute D. replace
A. abundant B. imagine C. solution D. driverless
III/ Choose the best option (3p)
I think perhaps we ______ flying cars soon.
A. will have B. will be having C. are going to have D. are having
Does that red motorbike belong to your mother? - No, ______ is white.
A. she B. her C. hers D. mine
We should try to make the world greener by using vehicles that are ______ .
A. environmental friendly B. environmentally friendly
C. friendly environment D. friendly environmental
Mai usually goes to school ______ bus but yesterday she came ______ her dad’s car.
A. in / on B. on / in C. by / in D. by / by
At this time next week, we ______ a wind turbine in our garden.
A. install B. have installed C. will install D. will be installing
Natural gas is a non-renewable source of energy and it may ______ soon.
A. run out B. run down C. use up D. use over
IV/ Give the correct form of the words in brackets (2p)
We couldn’t see the airplane because it ________disappeared_____ behind the cloud. (appear)
Your idea is really ____imaginative_________ , however, I don’t think it will come true soon. (imagine)
Vesak Day is a _______religious______ festival for those who follow Buddhism. (religion)
The traffic in some cities is so _____chaostic________ that it is difficult to see a solution. (chaos)
V/ Write questions for the underlined parts (1.5p)
The highlight of the festival is the tomato fight.
The Songkran Festival is usually celebrated between 13 and 16 of April.
It costs about $500 to join Glastonbury Festival.
VI/ Rewrite the following sentences, beginning with the given words (1.5p)
We will plant more trees to reduce the carbon dioxide.
More trees will be planted by us to reduce the carbon dioxide
I hope they will choose John for the school’s football team.
I hope John will be chosen for the school's football team
The local government will build a power station here next year.
A power station will be built here by the local government next year
