copy trên mạng thì cần gì phải đọc đề bài :))

Đặt f(x) = ax³ + x² - x + b

       g(x) = x² + 3x + 2 = ( x + 1 )( x + 2 )

       h(x) là thương trong phép chia f(x) cho g(x)

f(x) chia hết cho g(x) <=> f(x) = g(x).h(x)

<=> ax³ + x² - x + b = ( x + 1 )( x + 2 ).h(x) (*)

Với x = -1 => (*) <=> -a + 2 + b = 0 => -a + b = -2 (1)

Với x = -2 => (*) <=> -8a + 6 + b = 0 => -8a + b = -6 (2)

Từ (1) và (2) ta có hệ \(\hept{\begin{cases}-a+b=-2\\-8a+b=-6\end{cases}}\)Giải hệ thu được a = 4/7 và b = -10/7

Vậy a = 4/7 và b = -10/7

Gọi thương của phép chia là B(x)

⇒ x3+ax+b=(x2+x-2).B(x)

⇒x3+ax+b=(x+2)(x-1) . B(x)

Vì đẳng thức trên luôn đúng với mọi x nên ta thay x=1,x=-2

⇒ $\{\begin{array}{c}1+a+b=0\\ -8-2a+b=0\end{array}$

$\Rightarrow \{\begin{array}{c}a=-3\\ b=2\end{array}$

Với a=-3,b=2 thì x3+ax+b chia hết x2+x-2

Đề yêu cầu gì ạ ?

phân tích thành nhân tử

Rearrange the words to make meaningful sentences.

1. exported / many / last year / rice / how / to/ Japan / tons / were / of / ?

How many tons of rice were exported to Japan last year?

2. trees / planting / on / the boys / the hill / group / are / the / in / volunteer / .

 The boys in the volunteer group are planting trees on the hill.

3. rain / heavy / from / prevented / the / playing / us / soccer.

The heavy rain prevented us from playing soccer.

4. if / he / me / some / asked / I / money / could / then / lend / him /

If I asked him some money, he could lend me then.

5. design / to send / friends / someone / greetings / Englishman / a card / Christmas / to / an / his / had /.

 An Englishman had someone design a card to send Christmas greetings to his friends.

6. Le Lai Street / are/ living / they / in / at / An Giang / their / with /children / 186.

They are living with their children at 186 Le Lai Street in An Giang.

7. uncle / spent / most / their /of /the /violin / pracing / his time / in / room /music /the/.

 Their uncle spent most of his time pracing the violin in the music room.

8. which / us / tells / sentence / that / more / than / is / she / her / beautiful / sister /?

 Which sentence tells us that she is more beautiful than her sister?

9. his / friends / old / un / he / is / impolite / very /.

Un his old friends, he is very impolite.

10. going / fatherland / month / Kenny / his / is / family / next / visit / with / his / to /.

 Kenny is going to visit his fatherland with his family next month.

11. colleagues / go / he / to / to / weekend / and / don’t / have / at / work / the / his /.

 He and his colleagues don’t have to go to work at the weekend.

12. there / she / near / wanted / a / here / was / museum / know / to / if /.

She wanted to know if there was a museum near here.

13. hold / going / their / are / they / tomorrow / party / house / at / to / a /.

They are going to hold a party at their house tomorrow.

14. going / aren’t / are / boys / the / the / they / canteen / to / school /?

 The boys are going to the school canteen, aren’t they?

15. for / you’ll / meeting / late / be / the / if / bed / to / soon / don’t / you / go

⇒⇒ If you don’t go to bed soon, you’ll be late for the meeting.

Để lập CTHH của các chất thì em cần nắm vững hóa trị của nguyên tố và nhóm nguyên tố.

Tổng quát: A có hóa trị x, B hóa trị y => CT: A_yB_x (x và y là hệ số tối giản)

Ví dụ:

Na hóa trị I, (SO₄) hóa trị II => CT: Na₂SO₄

Al hóa trị III, (PO4) hóa trị III => CT: AlPO₄ (hệ số là 3:3 , tối giản đi sẽ được 1:1)

Để lập CTHH của các chất thì em cần nắm vững hóa trị của nguyên tố và nhóm nguyên tố.

Tổng quát: A có hóa trị x, B hóa trị y => CT: A_yB_x (x và y là hệ số tối giản)

Ví dụ:

Na hóa trị I, (SO₄) hóa trị II => CT: Na₂SO₄

Al hóa trị III, (PO4) hóa trị III => CT: AlPO₄ (hệ số là 3:3 , tối giản đi sẽ được 1:1)

Chào em, em tham khảo nhé!

Câu 1:Sửdụngthì HTHT đểhoànthànhcáccâusau: (5pts)

     1. I/know/her/five/months. => I have known her for five months.

     2.They/not/meet/Nam/ten/years. => They haven't met Nam for ten years.

     3. My/brother/live/there/last/summer. => My brother has lived there since last summer.

     4. I/learn/English/three/years. => I have learned English for three years.

     5. She/not come back here/a long time. => She hasn't come back here for a long time.

Câu 2:Chia độngtừtrongngoặc: (2.5pts)

1.     Nam hates (do) … the ironing. to do

2.     They (live) … here for six months. have lived

3.     She asked me (close) … the door. to close

4.     How long (play) … the guitar. have you played

5.     She enjoys (listen) … to music at weekend. listening

Chúc em học tốt và có những trải nghiệm tuyệt vời tại olm.vn!

ok\(\sqrt{ }\)

tự kết luận nhé ! 

a, \(\frac{3x}{x-2}-\frac{x}{x-5}=\frac{3x}{\left(x-2\right)\left(5-x\right)}\)ĐK : \(x\ne2;5\)

\(\Leftrightarrow\frac{3x}{x-2}+\frac{x}{5-x}=\frac{3x}{\left(x-2\right)\left(5-x\right)}\)

\(\Leftrightarrow\frac{3x\left(5-x\right)+x\left(x-2\right)}{\left(x-2\right)\left(5-x\right)}=\frac{3x}{\left(x-2\right)\left(5-x\right)}\)

\(\Rightarrow15x-3x^2+x^2-2x=3x\Leftrightarrow-2x^2+10x=0\)

\(\Leftrightarrow-2x\left(x-5\right)=0\Leftrightarrow x=0\left(tm\right);x=5\left(ktm\right)\)

b, \(\frac{13}{\left(x-3\right)\left(2x+7\right)}+\frac{1}{2x+7}=\frac{6}{\left(x-3\right)\left(x+3\right)}\)ĐK : \(x\ne\pm3;-\frac{7}{2}\)

\(\Leftrightarrow\frac{13\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(2x+7\right)}+\frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(2x+7\right)}=\frac{6\left(2x+7\right)}{\left(x-3\right)\left(x+3\right)\left(2x+7\right)}\)

\(\Rightarrow13x+39+x^2-9=12x+42\Leftrightarrow x-12+x^2=0\)

\(\Leftrightarrow\left(x-3\right)\left(x+4\right)=0\Leftrightarrow x=3\left(ktm\right);x=-4\left(tm\right)\)

c, \(1+\frac{x}{3-x}=\frac{5x}{\left(x+2\right)\left(3-x\right)}+\frac{2}{x+2}\)ĐK : \(x\ne3;-2\)

\(\Leftrightarrow\frac{\left(x+2\right)\left(3-x\right)}{\left(x+2\right)\left(3-x\right)}+\frac{x\left(x+2\right)}{\left(3-x\right)\left(x+2\right)}=\frac{5x}{\left(x+2\right)\left(3-x\right)}+\frac{2\left(3-x\right)}{\left(x+2\right)\left(3-x\right)}\)

\(\Rightarrow3x-x^2+6-2x+x^2+2x=5x+6-2x\)

\(\Leftrightarrow3x+6=3x+6\Leftrightarrow0=0\) Vậy phương trình vô nghiệm 

a) ĐKXĐ : \(x\ne-2;x\ne5\)

\(\frac{7}{x+2}=\frac{3}{x-5}\)

<=> 3(x + 2) = 7(x - 5)

<=> 3x + 6 = 7x - 35

<=> 4x = 41

<=>x = 41/4 (tm)

Vậy x = 41/4 là ngiệm phương trình

b) ĐKXĐ \(x\ne\pm3\)

\(\frac{2x-1}{x+3}=\frac{2x}{x-3}\)

<=> \(\frac{\left(2x-1\right)\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}=\frac{2x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)

<=> (2x - 1)(x - 3) = 2x(x + 3)

<=> 2x² - 7x + 3 = 2x² + 6x

<=> 13x = 3

<=> x = 3/13 (tm)

Vậy x = 3/13 là nghiệm phương trình

c) ĐKXĐ : \(x\ne-7;x\ne1,5\)

Khi đó \(\frac{3x-2}{x+7}=\frac{6x+1}{2x-3}\)

<=> \(\frac{\left(3x-2\right)\left(2x-3\right)}{\left(x+7\right)\left(2x-3\right)}=\frac{\left(6x+1\right)\left(x+7\right)}{\left(x+7\right)\left(2x-3\right)}\)

<=> (3x - 2)(2x - 3) = (6x + 1)(x + 7)

<=> 6x² - 13x + 6 = 6x² + 43x + 7

<=> 56x = -1

<=> x = -1/56 (tm) 

Vậy x = -1/56 là nghiệm phương trình

d) ĐKXĐ : \(x\ne\pm1\)

Khi đó \(\frac{2x+1}{x-1}=\frac{5\left(x-1\right)}{x+1}\)

<=> \(\frac{\left(2x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{5\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}\)

<=> (2x + 1)(x + 1) = 5(x - 1)²

<=> 2x² + 3x + 1 = 5x² - 10x + 5

<=> 3x² - 13x + 4 = 0

<=> 3x² - 12x - x + 4 = 0

<=> 3x(x - 4) - (x - 4) = 0

<=> (3x - 1)(x - 4) = 0

<=> \(\orbr{\begin{cases}3x-1=0\\x-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}\left(tm\right)\\x=4\left(tm\right)\end{cases}}\)

Vậy x \(\in\left\{\frac{1}{3};4\right\}\)là nghiệm phương trình

e) ĐKXĐ : \(x\ne1\)

Khi đó \(\frac{4x-5}{x-1}=2+\frac{x}{x-1}\)

<=> \(\frac{3x-5}{x-1}=2\)

<=> 3x - 5 = 2(x - 1) 

<=> 3x - 5 = 2x - 2

<=> x = 3 (tm) 

Vậy x = 3 là nghiệm phương trình

f) ĐKXĐ : \(x\ne-1\)

 \(\frac{1-x}{x+1}+3=\frac{2x+3}{x+1}\)

<=> \(\frac{3x+2}{x+1}=3\)

<=> 3x + 2 = 3(x + 1)

<=> 3x + 2 = 3x + 3

<=> 0x = 1

<=> \(x\in\varnothing\)

Vậy tập nghiệm phương trình S = \(\varnothing\)

g) ĐKXĐ : \(x\ne2\)

Khi đó \(\frac{1}{x-2}+3=\frac{x-3}{2-x}\)

<=>\(\frac{x-2}{x-2}=3\)

<=> (x - 2) = 3(x - 2)

<=> x - 2 = 3x - 6

<=> -2x = -4

<=> x = 2 (loại) 

Vậy tập nghiệm phương trình S = \(\varnothing\)

h) ĐKXĐ : \(x\ne7\)

Khi đó \(\frac{1}{7-x}=\frac{x-8}{x-7}-8\)

<=> \(\frac{x-7}{x-7}=8\)

<=> x - 7 = 8(x - 7)

<=> x - 7 = 8x - 56

<=> 7x = 49

<=> x = 7 (loại)

Vậy tập nghiệm phương trình S = \(\varnothing\)

i) ĐKXĐ : \(x\ne0;x\ne6\)

Ta có : \(\frac{x+6}{x}=\frac{1}{2}+\frac{15}{2\left(x-6\right)}\)

<=> \(\frac{x+6}{x}-\frac{15}{2\left(x-6\right)}=\frac{1}{2}\)

<=> \(\frac{2\left(x+6\right)\left(x-6\right)}{2x\left(x-6\right)}-\frac{15x}{2x\left(x-6\right)}=\frac{1}{2}\)

<=> \(\frac{2x^2-72-15x}{2x\left(x-6\right)}=\frac{1}{2}\)

<=> 4x² - 144 - 30x = 2x(x - 6) 

<=> 2x² - 18x - 144 = 0

<=> x² - 9x - 72 = 0

<=> x² - 9x + 81/4 - 72- 81/4 = 0

<=> \(\left(x-\frac{9}{2}\right)^2-\frac{369}{4}=0\)

<=> \(\left(x-\frac{9}{2}+\sqrt{\frac{369}{4}}\right)\left(x-\frac{9}{2}-\sqrt{\frac{369}{4}}\right)=0\)

<=> \(\orbr{\begin{cases}x=\frac{9}{2}-\sqrt{\frac{369}{4}}\\x=\frac{9}{2}+\sqrt{\frac{369}{4}}\end{cases}}\)(tm)

Vậy x \(\in\left\{\frac{9}{2}-\sqrt{\frac{369}{4}};\frac{9}{2}+\sqrt{\frac{369}{4}}\right\}\)