mk chắc chắn 100% là 99m<9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

Gọi d là ước của 2 số: 3a+7&4a+9

+)3a+7\(⋮\)d

=>4.(3a+7)\(⋮\)d

=>12a+28\(⋮\)d(1)

+)4a+9\(⋮\)d

=>3.(4a+9)\(⋮\)d

=>12a+27\(⋮\)d(2)

Từ (1) và(2) suy ra(12a+28)-(12a+27)\(⋮\)d

                      =>12a+28-12a-27\(⋮\)d

                        =>1\(⋮\)d

                       =>d=1

Vì d=1 nên 3a+7&4a+9 là 2 số ntố cùng nhau

Chúc bn học tốt

a) \(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{n\left(n+1\right)}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{n}-\frac{1}{n+1}=1-\frac{1}{n+1}\)

b) \(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{n\left(n+1\right)\left(n+2\right)}\right)\)

         \(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{n\left(n+1\right)}-\frac{1}{\left(n+1\right)\left(n+2\right)}\right)=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{\left(n+1\right)\left(n+2\right)}\right)\)

\(=\frac{1}{4}-\frac{1}{2\left(n+1\right)\left(n+2\right)}\)

Ta có : \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)

\(=\left[xy\left(x+y\right)+xyz\right]+\left[yz\left(y+z\right)+xyz\right]+xz\left(x+z\right)\)

\(=xy\left(x+y+z\right)+yz\left(x+y+z\right)+xz\left(x+z\right)\)

\(=y\left(x+y+z\right)\left(x+z\right)+xz\left(x+z\right)\)

\(=\left(x+z\right)\left(xy+y^2+yz+xz\right)\)

\(=\left(x+z\right)\left(x+y\right)\left(y+z\right)\)

6²ⁿ=1296

6²ⁿ=6⁴

=>2n=4

        n=4:2

         n=2

Chúc bn học tốt

CALCULARTOR

Tên tia O x, ta có :

OA < OB ( vì 4 cm < 10 cm ) 

Suy ra : điểm A nằm giữa hai điểm O và B 

Suy ra : OA + AB = OB 

hay 4 + AB = 10

Suy ra : AB = 10 - 4 = 6 cm 

Vậy AB = 6 cm 

Vì M là trung điểm của đoạn OA nên:

OM = MA  = OA / 2 =4 / 2 = 2 cm

Vì điểm N là trung điểm của đoạn  OB nên:

AN = NB = AB / 2 = 6/2 = 3 cm 

Suy ra : MN = MA + AN = 2 + 3 = 5 cm 

Vậy MN = 5 cm

N là trung điểm của OB sao lại suy ra AN=NB=AB/2=6/2=3