Là do Albert Einstein đó bn

\(n^2+1⋮2n+1\)

\(\Leftrightarrow\exists k\inℕ^∗:n^2+1=k\left(2n+1\right)\)

\(\Leftrightarrow n^2-2kn+1-k=0\)

Có \(\Delta'=\left(-k^2\right)-\left(1-k\right)=k^2+k-1\)

Vì \(n\inℕ^∗\)nên \(\Delta'\) phải là số chính phương 

\(\Leftrightarrow\exists l\inℕ^∗:k^2+k-1=l^2\)

\(\Leftrightarrow4k^2+4k-4=4l^2\)

\(\Leftrightarrow\left(4k^2+4k+1\right)-4l^2=5\)

\(\Leftrightarrow\left(2k+1\right)^2-\left(2l\right)^2=5\)

\(\Leftrightarrow\left(2k+2l+1\right)\left(2k-2l+1\right)=5\)

 Vì \(k,l\inℕ^∗\) và \(2k+2l+1>2k-2l+1>0\) nên ta chỉ có 1 TH duy nhất là \(\left\{{}\begin{matrix}2k+2l+1=5\\2k-2l+1=1\end{matrix}\right.\) \(\Leftrightarrow k=l=1\)

 Khi đó \(n^2+1=2n+1\) 

 \(\Leftrightarrow n^2=2n\)

 \(\Leftrightarrow\left[{}\begin{matrix}n=0\left(loại\right)\\n=2\left(nhận\right)\end{matrix}\right.\)

 Vậy \(n=2\) là số nguyên dương duy nhất thỏa mãn ycbt.

b

1 I live in Hanoi, the capital of Vietnam
2 Have you ever forgotten to turn off your mobile in a cinema or concert
3 Singing is good for health
4 I am good at learning languages
5 Which sports do you enjoy watching

1 I live in Ha Noi, the capital of Vietnam

2 Have you ever forgot to turn of the mobile at the cinema or a concert?

3 Singing is good for your health

4 I am good at learning languages

5 Which sports do you enjoy watching?

ĐKXĐ: \(20-x^2>0\)

=>\(x^2< 20\)

mà x nguyên

nên \(x\in\left\{0;1;-1;2;-2;3;-3;4;-4\right\}\)

=>Có 9 số nguyên

Sửa chóp S.ABC bn nhé

1 Why did you have to go to school last Saturday
2 You shouldn't spend too much time playing games
3 The children must wear a uniform
4 You should say sorry to your parents
5 You shouldn't drink so much coffee
6 He doesn't have to apologize. He was absolutely right
7 We have to give him our answer today or we'll lose out on the contract
8 You should go and lie down
9 You don't have to learn all the new words
10 Do you have to attend every English lesson
11 Harry should take a holiday
12 You shouldn't leave a child unsupervised
13 You have to register in advance to take the course
14 You don't have to read all those books
15 You should spend more time with her