a, x = 2

b, x = 14

Lời giải:

$\overline{5x}+\overline{x5}=77$

$50+x+x\times 10+5=77$

$(50+5)+(x\times 10+x)=77$

$55+11\times x=77$

$11\times x=77-55=22$

$x=22:11=2$

Lời giải:

a. 

$16=2^4$

$24=2^3.3$

Suy ra ƯCLN(16,24)=2^3=8$

ƯC(16,24)=Ư(8)=$\left\{1; 2;4;8\right\}$

b.

$180=2^2.3^2.5$

$234=2.3^2.13$

Suy ra ƯCLN(180,234)=$2.3^2=18$

ƯC(180,234)=Ư(18)=$\left\{1;2;3;9;18\right\}$

c.

$60=2^2.3.5$

$90=2.3^2.5$

$135=3^3.5$

ƯCLN(60,90,135)=$2.3.5=30$

ƯC(60,90,135)=Ư(30)=$\left\{1;2;3;5;6;10;15;30\right\}$

Yêu cầu đề bài là gì bạn cần ghi chú rõ.

Lời giải:
ƯCLN(a,b)=2 nên đặt $a=2x, b=2y$ với $x,y$ là 2 số nguyên tố cùng nhau. 

$ab=48$

$2x.2y=48$

$xy=12$

Do $x,y$ là 2 số nguyên tố cùng nhau nên $(x,y)=(1,12), (3,4), (4,3), (12,1)$

$\Rightarrow (a,b)=(2,24), (6,8), (8,6), (24,2)$

\(a,-\dfrac{3}{4}+\dfrac{2}{7}+\left(-\dfrac{1}{4}\right)+\dfrac{3}{5}+\dfrac{5}{7}\)

\(=\left[\left(-\dfrac{3}{4}\right)+\left(-\dfrac{1}{4}\right)\right]+\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\dfrac{3}{5}\)

\(=-1+1+\dfrac{3}{5}\)

\(=\dfrac{3}{5}\)

\(b,\dfrac{6}{21}-\dfrac{-12}{44}+\dfrac{10}{14}-\dfrac{1}{-4}-\dfrac{18}{33}\)

\(=\dfrac{2}{7}+\dfrac{3}{11}+\dfrac{5}{7}+\dfrac{1}{4}-\dfrac{6}{11}\)

\(=\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\left(\dfrac{3}{11}-\dfrac{6}{11}\right)+\dfrac{1}{4}\)

\(=1-\dfrac{3}{11}+\dfrac{1}{4}\)

\(=\dfrac{43}{44}\)

`7/9+2/3:2-1/45`

`=7/9+2/3xx1/2-1/45`

`=7/9+1/3-1/45`

`=35/45+15/45-1/45=49/45`

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