A B C D K E F H

a, ABCD là hình thang (gt) => AB // CD (đn)

=> OA/OC = OB/OD (talet)                                          (1)

có AF // BC (gt) => FO/OB = AO/OC (talet) ; có BE // AD (gt) => OE/OA = OB/OD (talet) và (1)

=> FO/OB = OE/OA ; xét tg AOB 

=> FE // AB (talet đảo)

b, có DA // BE (Gt) ; ^DAO slt ^OEB ; ^ADO slt ^OBE 

=> ^DAO = ^OEB và ^ADO = ^OBE (đl)

xét tg ADO và tg EBO 

=> tg ADO đồng dạng với tg EBO (g-g)

=> AO/OE = DO/OB                  (2)

+ AB // FE (câu a) => AO/OE = AB/EF (talet) ; có AB // DC (Câu a) => DO/OB = CD/AB (talet) và (2)

=> AB/EF = CD/AB 

=> AB^2  = EF.CD 

c, kẻ AH _|_ BD ; CK _|_ BD

có S1 = OB.AH/2 ; S2 = OD.CK/2  => S1.S2 = OB.AH.OD.CK/4

CÓ S3 = AH.DO/2 ; S4 = CK.OB/2 => C3.C4 = OB.AH.OD.CK/4

=> S1.S2 = S3.S4

a, ( x-1)³= -27

=> x - 1 = -3

=> x = -2

b, ( 2x - 1)²=25 

=> 2x - 1 = 5 hoặc 2x - 1 = -5

=> 2x = 6 hoặc 2x = -4

=> x = 3 hoặc x = -2

c, ( x - 3/4)²= ( 1/2)⁶ 

=> (x - 3/4)^2 = 1/64

=> x - 3/4 = 1/8 hoặc x - 3/4 = -1/8

=> x = 7/8 hoặc x = 5/8

d, 2 ^x + 2 ^{x +2} = 80 

=> 2^x + 2^x.4 = 80

=> 2^x(1 + 4) = 80

=> 2^x.5 = 80

=> 2^x = 16

=> x = 4

e, 4^x + 4 ^{x + 3} = 4160 

=> 4^x(1 + 64) = 4160

=> 4^x.65 = 4160

=> 4^x = 64

=> x = 3

When is your mother birthday ??

My mother birthday is 31/1

What is the date today ?

Today is 7/9
 

My mother birthday is 12/2

Today is 7/9

\(=\frac{\sqrt{1}-\sqrt{2}}{\left(\sqrt{1}+\sqrt{2}\right)\left(\sqrt{1}-\sqrt{2}\right)}+\frac{\sqrt{2}-\sqrt{3}}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}+..+\frac{\sqrt{99}-\sqrt{100}}{\left(\sqrt{99}+\sqrt{100}\right)\left(\sqrt{99}-\sqrt{100}\right)}\)

\(=\frac{\sqrt{1}-\sqrt{2}}{-1}+\frac{\sqrt{2}-\sqrt{3}}{-1}+...+\frac{\sqrt{99}-\sqrt{100}}{-1}\)

\(=\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+...+\sqrt{100}-\sqrt{99}\)

\(=\sqrt{100}-\sqrt{1}=10-1=9\)

Xét \(\frac{1}{\sqrt{a}+\sqrt{a+1}}=\frac{\sqrt{a}-\sqrt{a+1}}{\left(\sqrt{a}+\sqrt{a+1}\right)\left(\sqrt{a}-\sqrt{a+1}\right)}=\frac{\sqrt{a}-\sqrt{a+1}}{a-\left(a+1\right)}=-\sqrt{a}+\sqrt{a+1}\)

Xét dãy tính: \(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\)

\(=-\sqrt{1}+\sqrt{2}-\sqrt{2}+\sqrt{3}-...-\sqrt{99}+\sqrt{100}\)

\(=-\sqrt{1}+\sqrt{100}=-1+10=9\)

\(\left(\frac{1}{125}\right)^3.2^6=\left(\frac{1}{125}\right)^3.2^{2.3}=\left(\frac{1}{125}\right)^3.\left(2^2\right)^3=\left(\frac{2^2}{125}\right)^3=\left(\frac{4}{125}\right)^3\)

Rearrange the words to make correct sentences 

1. are / very / the people / sunny / and / the weather / warm / has / and / been / friendly .

=> There people are very friendly and the weather has been sunny and warm .

2. vietnam / of / is / one / the / it / popular / most / tourist attractions / in .

=> It is one of the most popular tourist attactions in Vietnam .

3. will / my family and friends / buy / I / make / some / gift / pottery / a / to / for .

=> I will buy some pottery to make a gift for my family and friends .

Học tốt

a) \(\frac{2\sqrt{5}+b\sqrt{a}}{\sqrt{ab}}-\frac{1}{\sqrt{a}-\sqrt{b}}\)

\(=\frac{2\sqrt{5ab}+ab\sqrt{b}}{ab}-\frac{\sqrt{a}+\sqrt{b}}{a-b}\)

\(=\frac{\left(2\sqrt{5ab}+ab\sqrt{b}\right)\left(a-b\right)-\left(\sqrt{a}+\sqrt{b}\right)ab}{ab\left(a-b\right)}\)

\(=\frac{2a\sqrt{5ab}-2b\sqrt{5ab}+a^2b\sqrt{b}-ab^2\sqrt{b}-ab\sqrt{a}-ab\sqrt{b}}{ab\left(a-b\right)}\)

b) \(\left(1+\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\cdot\left(\frac{1+1+\sqrt{a}}{1-a^2}\right)^2\)

\(=\left(1+\frac{\left(\sqrt{a}-1\right)\sqrt{a}}{\sqrt{a}-1}\right)\cdot\left(\frac{2+\sqrt{a}}{\left(1-a\right)\left(1+a\right)}\right)^2\)

\(=\left(1+\sqrt{a}\right)\left[\frac{2+\sqrt{a}}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a\right)}\right]^2\)

\(=\frac{4+4\sqrt{a}+a}{\left(1-\sqrt{a}\right)^2\left(1+\sqrt{a}\right)\left(1+a\right)^2}\)  \(a\ge0;a\ne\pm1\)

Bổ sung đk của phần a: \(a,b>0;a\ne b\)

Số bi của Hùng lúc đầu là: \(17:\frac{4}{5}+6=27,25\)viên bi

Đề toang roi !

                                                                            Giải

  sau khi lấy ra, hùng còn số viên bi là : 

                     17*5=85[ viên ]

  Hùng có số viên bi là:

                      85+6= 91 [ viên ]

                            Đ/S: 91 viên bi

1. If my parents allowed me to go, I wouldn't have to stay at home.

2. If the computer hadn't broken down, I wouldn't have had to stop my work.

3. If she didn't love him, she wouldn't forgive he easily.

4. If you had often talked to them, they would have understood you.

5. If I had had a dictionary, I could have looked the word up.

6. If Sandra had got her camera, she could take a photo.

7. If I didn't have to work tomorrow evening, I would meet you.

8. If it hadn't been raining, we could have had lunch in the garden.

9. If Susan had got a watch, she wouldn't be often late for work.

10. If he didn't smoke forty cigarettes a day, he wouldn't cough a lot.

11. If I had a boat, I would sail around the world.

12. If they had had a garden, they would have grown vegetables.

13. If I had known his address, I would have given it to you.

14. If the doctor hadn't been so late, he could have seen many patients.

a) 

\(3x^2-x^3-9x+3x^2+27-9x=27-x^3\) 

\(-x^3+6x^2-18x+27=27-x^3\) 

\(6x^2-18x=0\) 

\(6x\left(x-3\right)=0\) 

\(\orbr{\begin{cases}6x=0\\x-3=0\end{cases}}\) 

\(\orbr{\begin{cases}x=0\\x=3\end{cases}}\) 

b) 

\(x^4-x^3y+x^3y-x^2y^2+x^2y^2-xy^3+xy^3-y^4=x^4-y^4\) 

\(x^4-y^4=x^4-y^4\) 

\(0=0\left(llđ\forall x\right)\) 

a) ( x² - 3x + 9 )( 3 - x ) = 27 - x³

<=> -x³ + 6x² - 18x + 27 = 27 - x³

<=> -x³ + 6x² - 18x + x³ = 27 - 27

<=> 6x² - 18x = 0

<=> 6x( x - 3 ) = 0

<=> \(\orbr{\begin{cases}6x=0\\x-3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=3\end{cases}}\)

b) Ta có VP = ( x² )² - ( y² )²

                    = ( x² - y² )( x² + y² )

                    = ( x - y )( x + y )( x² + y² )

                    = ( x - y )[ ( x + y )( x² + y² ) ]

                    = ( x - y )( x³ + xy² + x²y + y³ ) = VT

Vậy phương trình nghiệm đúng với mọi x, y ∈ R