Ta có : xy + x + y = -1

=> x(y + 1) + y + 1 = -1 + 1

=> (x + 1)(y + 1) = 0

=> \(\orbr{\begin{cases}x+1=0\\y+1=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=-1\\y=-1\end{cases}}\)(đpcm) 

Vậy nếu xy + x + y = - 1 thì có ít nhất 1 số bằng - 1

xy + x + y = -1

<=> xy + x + y + 1 = 0

<=> x( y + 1 ) + 1( y + 1 ) = 0

<=> ( x + 1 )( y + 1 ) = 0

\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\y+1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\y=-1\end{cases}}\) ( đpcm )

thì phân tích thành nhân tử là oke

\(x^2+x+1>0\)

\(\Leftrightarrow x^2+x+\frac{1}{4}+\frac{3}{4}>0\)

\(\Leftrightarrow\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\)*đúng*

Ta có:\(x^2+x+1=\left(x^2+x+\frac{1}{4}\right)+\frac{3}{4}=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\)

Vì\(\left(x+\frac{1}{2}\right)^2\ge0\forall x\in R\Rightarrow\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}>0\left(đpcm\right)\)

Dãy số trên có số hạng là:

(2016-2):2=1007 (số hạng)

là 2026 mà bn.

\(\frac{\left(81,624:4\frac{4}{3}-4,505\right)+125\frac{3}{4}}{\left[\left(\left(\frac{11}{25}\right)^2:0,08+3,53\right)^2-\left(2,75\right)^2\right]:\frac{13}{25}}\)

\(=\frac{\left(\frac{10203}{125}.\frac{3}{16}-\frac{901}{200}\right)+\frac{503}{4}}{\left[\left(\frac{121}{625}.\frac{25}{2}+\frac{353}{100}\right)^2-\frac{121}{16}\right].\frac{25}{13}}\)

\(=\frac{\left(15,3045-\frac{901}{200}\right)+\frac{503}{4}}{\left(\frac{14161}{400}-\frac{121}{16}\right).\frac{25}{13}}\)

\(=\frac{136,5495}{\frac{696}{13}}\)

\(=2,550493534\)

1)\(\left(-8\right)^2=64\)

2)\(\left(-1,25\right)^2=1,56\)

3) \(3^5=243\)

4) \(2^5:2^3\Leftrightarrow2^{5-3}=2^2\)

5) \(\left(-4\right)^2\times\left(-4\right)=\left(-4\right)^{2+1}=\left(-4\right)^3\)

6) \(\left(\frac{2}{3}\right)^3\times\left(\frac{2}{3}\right)^2=\left(\frac{2}{3}\right)^{3+2}=\left(\frac{2}{3}\right)^5\)

6,1. = 64

2 . = 1,56

3 . =243

4 , = 2² = 4

5  , (-4³) = -12

6, = 2/3 ⁵ = 22 / 213

Tổng số phần bằng nhau là:

4+5=9( phần)

1 phần có số tuổi là:

27 :9=3 (tuổi)

Tuổi em là:

3.4=12(tuổi)

Tuổi chị là:

3.5=15 (tuổi)

Đ/s :Em 12 tuổi

       Chị 15 tuổi

                                               Bài làm :

Tổng số phần bằng nhau là :

4+5=9 (Phần)

Tuổi em là :

27 : 9 x 4 = 12 (Tuổi)

Tuổi chị là :

27 - 12 =15 (Tuổi)

             Đáp số : Em:12 tuổi

                          Chị : 15 tuổi

Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

\(\frac{x+2}{5}< \frac{x+2}{3}+\frac{1}{2}\)

\(\Leftrightarrow\frac{6\left(x+2\right)}{30}< \frac{10\left(x+2\right)}{30}+\frac{15}{30}\)

\(\Leftrightarrow\frac{6x+12}{30}< \frac{10x+20}{30}+\frac{15}{30}\)

\(\Leftrightarrow6x+12< 10x+20+15\)

\(\Leftrightarrow6x-10x< 20+15-12\)

\(\Leftrightarrow-4x< 23\)

\(\Leftrightarrow x>-\frac{23}{4}\)

Vậy tập nghiệm của bất phương trình là \(x>-\frac{23}{4}\)

\(\frac{x+2}{4}-x< \frac{1}{3}\)

\(\Leftrightarrow\frac{3\left(x+2\right)}{12}-\frac{12x}{12}< \frac{4}{12}\)

\(\Leftrightarrow\frac{3x+6}{12}-\frac{12x}{12}< \frac{4}{12}\)

\(\Leftrightarrow3x+6-12x< 4\)

\(\Leftrightarrow3x-12x< 4-6\)

\(\Leftrightarrow-9x< -2\)

\(\Leftrightarrow x>\frac{2}{9}\)

Vậy tập nghiệm của bất phương trình là \(x>\frac{2}{9}\)

\(\frac{2x-1}{x+2}< 0\)( ĐKXĐ : \(x\ne-2\))

Xét hai trường hợp

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

2/ \(\hept{\begin{cases}2x-1>0\\x+2< 0\end{cases}}\Rightarrow\hept{\begin{cases}x>\frac{1}{2}\\x< -2\end{cases}}\)( loại )

Vậy tập nghiệm của bất phương trình là \(-2< x< \frac{1}{2}\)

Put the verbs in the brackets in the correct tenses form.

1. Nam looks brown. He was on holiday last week. He (get) ....got...... sunburnt.

2. Getting plenty of a rest is very good. It (help)...........helps...... you to avoid depression.

3. The Japanese (eat) ....eat......... a lot of fish, so they are intelligent.

4. If you wash you hands more, you (have) .....will have..... less chance of catching flu.

5. Eating carrots regularly (help) ...helps...... you see better.

6. It is very hot outside. Please (wear) ......wear..... a sun hat when you go out.

7. Do more exersise and you (feel) ...will feel........ healthier.

8. I don' t want (be) ......to be...... tired tomorrow, so I go to bed early.

9. Nowadays, I don' t feel well. I often (feel)... feel.. sick and weak.

10. People who (smile) ....smile ........ more are happier andthey live longer

II. Put the verbs in brackets in the correct tense form.

1. It is important (eat) .to eat.. well.
2. It (be) ..is. very cold today. You should wear your warm clothes when you (go) .. go . out to prevent cold.
3. Do morning exercise everyday and you'll (feel) ..feel .. better

4. I have a lot of homework to do this evening, so I (not have) .don't have.. time to watch the football match.
5. (Eat) eating ... junk food and inactivity (be)is ... the main causes of obesity.
6. I (have) .have.. a headache and I need to rest more.
7. I (have) ..have. a toothache so I (have to/see) .have to see.. the dentist
8. I have to take medicines because I (be) .am.. sick
9. Japanese (eat) .eat.. more fish instead of meat, so they (stay) .. stay . more healthy.
10. When you ( have) ... a fever, you (should/drink) ... more water and rest more have/should drink
11. A healthy diet (help) ... us feel healthier helps
12. Watching TV much (hurt) ... your eyes hurts

I. Give the correct form of the word given to complete the sentence.