Gọi số cần tìm là \(\overline{abc}\), trong đó a, b, c là các chữ số và a khác 0.

Nếu tăng chữ số hàng trăm lên n đơn vị đồng thời giảm chữ số hàng chục và chữ số hàng đơn vị đi n đơn vị thì ta được số:

\(\overline{\left(a+n\right)\left(b-n\right)\left(c-n\right)}\)

Theo bài ra ta có:

\(\overline{\left(a+n\right)\left(b-n\right)\left(c-n\right)}=n.\overline{abc}\)

\(100\left(a+n\right)+10\left(b-n\right)+c-n=n\left(100a+10b+c\right)\)

\(100a+10b+c-100na-10nb-nc+89n=0\)

\(100a\left(1-n\right)+10b\left(1-n\right)+c\left(1-n\right)+89n=0\)

\(\left(100a+10b+c\right)\left(1-n\right)=-89n\)

\(\overline{abc}\left(n-1\right)=89n\)

Do 89 là số nguyên tố nên \(\orbr{\begin{cases}\overline{abc}\inƯ\left(89\right)\\n-1\inƯ\left(89\right)\end{cases}}\)

Do \(\overline{abc}>100\) nên \(\overline{abc}\) không thể là ước 89.

Vậy nên \(n-1\inƯ\left(89\right)\)

Do n < 9 nên n - 1 = 1 hay n = 2.

Từ đó suy ra \(\overline{abc}=89.2=178\) 

Vậy số cần tìm là 178.

hỏi thầy

a) \(x^2-xy+y^2=3\)

\(\Leftrightarrow\left(x+y\right)^2=3\left(1+xy\right)\)

\(\Rightarrow xy\ge-1\).

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

\(\Leftrightarrow\left(x-y\right)^2=3-xy\)

\(\Rightarrow xy\le-1\)

Do vai trò \(x,y\)như nhau nên giả sử \(x\ge y\).

- \(xy=-1\Rightarrow x=1,y=-1\).

Thử lại thỏa mãn. 

- \(xy=0\Rightarrow\orbr{\begin{cases}x=0\\y=0\end{cases}}\)dễ thấy đều không thỏa. 

- \(xy=1\Rightarrow\orbr{\begin{cases}x=y=1\\x=y=-1\end{cases}}\)không thỏa. 

- \(xy=2\Rightarrow\orbr{\begin{cases}x=2,y=1\\x=-1,y=-2\end{cases}}\)thỏa. 

- \(xy=3\Rightarrow\orbr{\begin{cases}x=3,y=1\\x=-1,y=-3\end{cases}}\)không thỏa. 

b) \(x=0\Rightarrow y=\pm1\)thỏa mãn. 

\(x\ne0\):

 \(y^2=1+x+x^2+x^3+x^4\)

\(\Leftrightarrow4y^2=4+4x+4x^2+4x^3+4x^4\)

Ta có: \(4x^4+4x^3+4x^2+4x+4>4x^4+4x^3+x^2=\left(2x^2+x\right)^2\)

\(4x^4+4x^3+4x^2+4x+4< 4x^4+4x^3+9x^2+4x+4=\left(2x^2+x+2\right)^2\)

suy ra \(4y^2=\left(2x^2+x+1\right)^2\)

\(\left(2x^2+x+1\right)^2=4+4x+4x^2+4x^3+4x^4\)

\(\Leftrightarrow\orbr{\begin{cases}x=-1\\x=3\end{cases}}\)

Tử đây suy ra \(y\).

Trra lời:

Bn tham khỏa nhé:

https://thayhieu.net/de-thi-thu-ngu-van-huong-moi-va-bai-lam-mau/

~HT~

PTBĐ chính: Tự sự

27,89   nha

27,89 

-HT-

ta có: A+B+C=180⁰(tổng 3 góc tam giác) mà C=90⁰(vuông ở C ) suy ra A+B=90⁰ mà B=2A suy ra A+2A=90⁰ suy ra A=30⁰ suy ra B =60⁰

a, vì DCA kề bù với C suy ra DCA +C=180⁰ mà C=90⁰suy ra DCA=90⁰ suy ra DCA=C

xét tam giác ADC và ACB: DCA=C, CD=CB, AC cạnh chung suy ra tam giác ADC = ACB suy ra DAC=CAB và AD=AB

b, xét tam giác AMC, ANC:  DAC=CAB, AC cạnh chung, AM=AN suy ra  tam giác AMC=ANC suy ra MC=CN

c,xét tam giác MAC,NAC: DAC=CAB, AI cạnh chung , AM=AN suy ra  tam giác MAC=NAC suy ra AIM=AIN và IM=IN

d, vì AIM kề bù IAN suy ra AIM+IAN=180⁰ mà AIM=AIN suy ra AIN+AIN=180⁰ suy ra AIN=90⁰

vì AIN=90⁰ và C=90⁰ suy ra MN //BD

k ???????

Dear Liu!

Last time I told you that I had been thinking about pursuing higher education in the UK. I got started to learn the process of applying for a university in London some time ago. Now I have some questions for you. 

First, what is the procedure for applying for a student visa? Of course. I have to submit an application but what other documents are required? How long does it take me to obtain my student visa? It is important to plan time to wait for visa processing because the time between finding out I have been accepted to go and leaving may be very close together. Second, do 1 have to present my financial documents; for example proof of funds, to prove that I am able to pay for my education? And last, do I need to obtain the International Certificate of Vaccination? Is it required that I have certain vaccinations before I go? What are they? After all. can you make me a checklist: what I should bring and what I should leave at home? 

I wish you and your family the best. I look forward to hearing from you soon. 

                                                                                                     Regards, 

                                                                                                     Mai Anh

Mong cô duyệt bài ạ:

Dear Duc Son,

Last time I told you that I had been thinking about pursuing higher education in the UK. I got started to learn the process of applying for a university in London some time ago. Now I have some questions for you.

First, what is the procedure for applying for a student visa? Of course. I have to submit an application but what other documents are required? How long does it take me to obtain my student visa? It is important to plan time to wait for visa processing because the time between finding out I have been accepted to go and leaving may be very close together. Second, do 1 have to present my financial documents; for example proof of funds, to prove that I am able to pay for my education? And last, do I need to obtain the International Certificate of Vaccination? Is it required that I have certain vaccinations before I go? What are they? After all. can you make me a checklist: what I should bring and what I should leave at home?

I wish you and your family the best. I look forward to hearing from you soon.

Regards,

Dang Phong

10 nha

kobit

hahaha

ngan 1:400

ngan 2:600

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