Để \(\frac{x^2+7}{x+1}\)nhận giá trị nguyên thì \(x^2+7⋮x+1\left(1\right)\)

+)Ta có:\(x+1⋮x+1\)

\(\Rightarrow x.\left(x+1\right)⋮x+1\)

\(\Rightarrow x^2+x⋮x+1\left(2\right)\)

+)Từ (1) và (2)

\(\Rightarrow\left(x^2+x\right)-\left(x^2+7\right)⋮x+1\)

\(\Rightarrow x^2+x-x^2-7⋮x+1\)

\(\Rightarrow x-7⋮x+1\left(3\right)\)

+)Ta lại có:\(x+1⋮x+1\left(4\right)\)

+)Từ (3) và (4)

\(\Rightarrow\left(x+1\right)-\left(x-7\right)⋮x+1\)

\(\Rightarrow x+1-x+7⋮x+1\)

\(\Rightarrow8⋮x+1\)

\(\Rightarrow x+1\in\left\{\pm1;\pm2;\pm4;\pm8\right\}\)

\(\Rightarrow x\in\left\{-2;0;-3;1;-5;3;-9;7\right\}\in Z\)

Vậy \(x\in\left\{-2;0;-3;1;-5;3;-9;7\right\}\)

Chúc bn học tốt

1.A
2.P
3.P
4.A
5.P

1 They grow coffee in more than 50 countries around the world__A________

2 The book was bought yesterday____P_____

3 Tim was invited to Kate"s birthday party ___P____

4 She feeds her dogs twice a day___A_______

5 My keys were lost yesterday__P__

a/ xét 2 tam giác AMB và CMK có:

AM = MC (M là t/đ AC)

góc KMC = góc BMA (đối đỉnh)

MK = MB (gt)

=> tam giác AMB = tam giác CMK (c.g.c)

=> góc MAB =  góc MCK = 90 độ hay KC vuông AC (đpcm)

b. xét hai tam giác AMK và CMB có:

AM = MC (M là t/đ AC)

góc AMK = góc CMB (đối đỉnh)

MK = MB (gt)

=> tg AMK = tg CMB (c.g.c)

=> góc AKM = góc CBM mà hai góc này ở vị trí sole trong nên AK // BC (đpcm)

1.A

2.A

3.A

1 It is dangerous to ride a motorbike without a...................

A) helmet

B) triangle

C) tricycle

D) cirlcle

2 In Ha Noi, during rush hour , some road users ride their motorbikes on the .....................

A) driving licence

B) lane

C) pavement

D) seat belt

3 Traffic is terrible  during the ..............when everyone is in a hurry to get to work or come back home
A) traffic light
B) road  sign

C) traffic rule

D) rush hour

học tốt

b) \(\left(x-\frac{1}{2}\right)\left(1+5x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{2}=0\\1+5x=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=0+\frac{1}{2}=\frac{1}{2}\\5x=-1\Rightarrow x=\frac{-1}{5}\end{cases}}\)

vậy............................................

a) 42 + 3/7 . | 3x - 1 | = 12

<=> 3/7 . | 3x - 1 | = 12 - 42

<=> 3/7 . | 3x - 1 | = -30

<=> | 3x - 1 | = -30 . 3/7

<=> | 3x - 1 | = -90/7 (vô lí)

b) (x - 1/2)(1 + 5x) = 0

<=> \(\hept{\begin{cases}x-\frac{1}{2}=0\\1+5x=0\end{cases}}\) <=> \(\hept{\begin{cases}x=\frac{1}{2}\\x=-\frac{1}{5}\end{cases}}\)

c) | 2x - 1 | = | x + 2 |

<=> \(\hept{\begin{cases}2x-1=x+2\\2x-1=-x-2\end{cases}}\) <=> \(\hept{\begin{cases}2x-x=1+2\\2x+x=1-2\end{cases}}\) <=> \(\hept{\begin{cases}x=3\\x=-\frac{1}{3}\end{cases}}\)

\(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)

\(\frac{1}{2^2}< \frac{1}{1\cdot2}\)

\(\frac{1}{3^2}< \frac{1}{2\cdot3}\)

\(\frac{1}{4^2}< \frac{1}{3\cdot4}\)

...

\(\frac{1}{100^2}< \frac{1}{99\cdot100}\)

\(\Rightarrow A< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

\(\Rightarrow A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow A< 1-\frac{1}{100}=\frac{99}{100}\) ; \(\frac{99}{100}< \frac{3}{4}\)

\(\Rightarrow A< \frac{3}{4}\)

Nguyễn Phương Uyên Chị này học giỏi ghê á, \(\frac{99}{100}=0,99< \frac{3}{4}=0,75\)

Quá giỏi luôn nha, \(0,99< 0,75\) ?? Woww giờ em mới biết :))

Sửa thành chứng minh △AMB = △AMC

a, Xét △BAM và △CAM

Có: AB = AC (△ABC cân tại A)

  ^BAM = ^CAM (gt)

   AM là cạnh chung

=> △BAM = △CAM (c.g.c)

b, Xét △ABH vuông tại H và △ACK vuông tại K

Có: AB = AC (cmt)

      ^BAC là góc chung

=> △ABH = △ACK (ch-gn)

=> BH = CK (2 cạnh tương ứng)

Số đo mỗi bên à :

 \(\frac{4}{5}:4=\frac{1}{5}\left(dm\right)\)

Đ/s :\(\frac{1}{5}dm\)

Số đo của mỗi bên là :

\(\frac{5}{4}:4=\frac{1}{5}\left(dm\right)\)

Đ/S: \(\frac{1}{5}dm\)

hok tốt

1 There did not.....use to...... be many shops on this street before

2 We..used to..... go to work by car

3 Did they..use to.......cycle to work?
4 She ,,,,,,used to........work for a foreign company

5 My friend didn't........use to....ride a tricycle when he was a child

6 Did you..use to........ play marbles when you were small?

học tốt

1. use to

2. used to

3. use to

4. used to

5. use to

6. use to