\(\left(x-2\right)\left(x^2+2x+4\right)-\left(x-1\right)^3+7\)

\(=x^3-8-\left(x^3-3x^2+3x-1\right)+7\)

\(=x^3-8+7-x^3+3x^2-3x+1\)

\(=\left(x^3-x^3\right)+\left(7+1-8\right)+3x^2-3x\)

\(=3x^2-3x=3x\left(x-1\right)\)

\(x\left(x+2\right)\left(2-x\right)+\left(x+3\right)\left(x^2-3x+9\right)\)

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

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

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

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

\(=4x+9\)

Để AA là số chính phương ⇒26n+17=t2(t∈N)⇒26n+17=t2(t∈N)

⇒26n+13=t2−4⇒26n+13=t2−4

⇒13(2n+1)=(t−2)(t+2)(1)⇒13(2n+1)=(t−2)(t+2)(1)

⇒(t−2)(t+2)⋮13⇒(t−2)(t+2)⋮13⇒⎡⎣t−2⋮13t+2⋮13⇒[t−2⋮13t+2⋮13

*)Xét t+2⋮13⇒t+2=13m(m∈N)t+2⋮13⇒t+2=13m(m∈N)⇒t=13m−2⇒t=13m−2

Thay vào (1)(1)⇒13(2n+1)=13m(13m−4)⇒13(2n+1)=13m(13m−4)

⇒2n+1=m(13m−4)⇒n=13m2−4m−12⇒2n+1=m(13m−4)⇒n=13m2−4m−12

*)Xét t−2⋮13⇒t−2=13m(m∈N)t−2⋮13⇒t−2=13m(m∈N)⇒t=13m+2⇒t=13m+2

Thay vào (1)(1)⇒13(2n+1)=13m(13m+4)⇒13(2n+1)=13m(13m+4)

⇒2n+1=m(13m+4)⇒2n+1=m(13m+4)⇒n=13m2+4m−12⇒n=13m2+4m−12

Vậy.....

chúc bạn hok tốt

đặt \(\hept{\begin{cases}n+5=x^2\\n+30=y^2\end{cases}\left(x;y\in N;x,y>0\right)}\)

\(\Leftrightarrow y^2-x^2=25\Leftrightarrow\left(y-x\right)\left(y+x\right)=1.25\)(vì x,y thuộc N, x,y>0)

lại có y-x<y+x nên \(\hept{\begin{cases}y+x=1\\y+x=25\end{cases}\Leftrightarrow\hept{\begin{cases}y=13\\x=12\end{cases}}}\)

thay vào ta được n=139 thỏa mãn

anh có thể k cho em được ko em cần thêm k đúng

Dễ thôi :D 

Đặt \(\frac{n\left(2n-1\right)}{26}=q^2\) Khi đó ta được:\(n\left(2n-1\right)=26q^2\)

Do VP chẵn nên n phải là số chẵn, đặt n = 2k ( k tự nhiên )

\(\Rightarrow k\left(4k-1\right)=13q^2\)

Mặt khác \(\left(k;4k-1\right)=1\Rightarrow\hept{\begin{cases}k=a^2\\4k-1=13b^2\end{cases}}\left(h\right)\hept{\begin{cases}k=13b^2\\4k-1=a^2\end{cases}}\) với a, b là các số tự nhiên

\(TH1:k=a^2;4k-1=13b^2\Rightarrow4k=13b^2+1=12b^2+b^2+1\)

Vì vậy \(b^2\equiv3\left(mod4\right)\) vô lý vì b² phải là số chính phương.

\(TH2:k=13b^2;4k-1=a^2\Rightarrow4k=a^2+1\) tương tự thì không tồn tại.

Vậy không tồn tại n nguyên dương sao cho \(\frac{n\left(2n-1\right)}{26}\) là số chính phương

Bài làm:

Ta có: \(A=64-\left(x-4\right)\left(x^2+4x+16\right)\)

\(A=64-x^3+64\)

\(A=128-x^3\)

Tại \(x=-\frac{1}{2}\) ta được:

\(A=128-\left(-\frac{1}{2}\right)^3=\frac{1025}{8}\)

A = 64 - ( x - 4 )( x² + 4x + 16 )

A = 64 - ( x³ + 4x² + 16x - 4x² - 16x - 64 )

A = 64 - ( x³ - 64 )

A = 64 - x³ + 64

A = -x³ + 128

Thế x = -1/2 vào A ta được :

A = -(-1/2)³ + 128 = 1/8 + 128 = 1025/8

a)tứ giác ABMC là hình chữ nhật (vì là hbh có 1 góc vuông)

b)Xét tam giác ABC có:BE=AE,DB=DC=>ED là đường trung bình của tam giác ABC

=>ED//AC=>ED//AF         (1)

C/M tương tự DF//AE(DF là đường trung bình của tam giác BAC)           (2)

Từ (1),và (2)=>EDFA là hbh.Mà BAC^=90độ=>EDFA là hcn(hbh có 1 góc vuông)

d)ĐK:tam giác ABC là tam giác cân=>AB=AC      (4)

Vì AE=1/2AB,AF=1/2AC               (5)                     

   Từ (4) và (5)=>AE=AF=>ADEF là hình vuông(vì AEDF mik đã c/m là hcn ở ý b rồi)(hcn có 2 cạnh kề bắng nhau là hình vuông)

Never is never

nếu bạn thật sự cần:

Không bao giờ là qua level -> never next level

ko tìm đc bn ơi

thiếu đề r

Gọi 2 số cần tìm là ab và 7ab 

ta có :(ab+7ab):2=428

=>ab+7ab=428.2=856

=>ab+700+ab=856

=>ab+ab=856-700=156

=>ab.2=156

=>ab=156:2=78

    vậy ab=78       và         7ab=778

5,432 x 5,39 - 4,63 : 2,25 + 11,6 

Trả lời:

  5,432 x 5,39 - 4,63 : 2,25 + 11,6 

= 29,27848 - 2,057... + 11,6

=27,220702... +11,6 

=38,820702

học tốt

Ta có: 5,432 x 5,39 - 4,63 : 2,25 + 11,6

= 29,27848 - 2,0577... + 11,6

=27,22078 + 11,6

=38,82078

When I was a student, I used to live in Hanoi.So I was the person who always got traffic jams. Nowadays, althought the traffic in Hanoi has been improved ,it still is one of the most serious problems in our society. In my opinion, there are some following ways to reduce the traffic jams. Firstly, The government should build more motorways because many streets and roads are narrow, a lot of transports share one road so it is easy to cause accidents and traffic jams. Secondly, a law about driving in city center should be given. Motorists driving in city center must be charged strictly. There are too much motocycles in the city, many motorisrs are too young, they don't have driving license, they don't understand the law or they don't obey the law seriously . The government should encourage people to use the puplic transport by discouring the price for someone who always uses public transport, especially for students ,workers, etc, opening more bus routes,maybe build the subway. I think subway is the best way to reduce the traffic jams. Things we should do immedietely are educating people from early age, issueing a law in traffic, banning stricly the person who don't obey the law. In conclusion, we should be aware of disadvantages of traffic jams. It affects on every sides of our life.

Học Tốt

Nowaday, traffic problem is the biggest problem that many people care about. In VN, I think the city where have the worst traffic is Ha noi. 
The first problem is the traffic jam here. Why? In the rush hours of the day, there're too many people using the road. Last year, in 2013, many bridges was built so it happen less but in order to stop this, a kind of small car should be invented, people should go to works by buses instead of going by motorbikes... 
The second one, as you know, the roads in VN is not as big and clean as the roads in the big countries. They're narrow, bumpy and some dirty so it’s really hard for the road users to drive safely. I think we should raise money to make the road in VN better and better. 
But everyone knows that Vietnamese people are not respect and don’t follow the traffic rules. That’s the biggest reason for everything. They wear the helmet that not strong enough to keep they safe if the accident may happen, they ride too fast on the small roads… The traffic will never can be improve if they keep doing this. 
At the end, I hope the traffic in VN will improve more.

Để \(\frac{6a-13}{5a-17}\inℤ\)

=> \(6a-13⋮5a-17\)

=> 5(6a - 13) \(⋮\)5a - 17

=> 30a - 65 \(⋮\)5a - 17

=> 30a - 102 + 37  \(⋮\)5a - 17

=> 6(5a - 17) + 37  \(⋮\)5a - 17

Vì \(6\left(5a-17\right)⋮5a-17\)

=> 37 \(⋮\)5a - 17

=> 5a - 17 \(\in\)Ư(37)

=> \(5a-17\in\left\{1;-1;37;-37\right\}\)

=> a \(\in\left\{\frac{18}{5};\frac{16}{5};\frac{54}{5};-4\right\}\)

Vì a là số tự nhiên => a \(\in\varnothing\)

thank bạn xyz nha