a) \(x-\frac{5}{7}=\frac{1}{9}\Rightarrow x=\frac{1}{9}+\frac{5}{7}\Rightarrow x=\frac{52}{63}\)

b) \(\frac{-3}{7}-x=\frac{4}{5}+\frac{-2}{3}\Rightarrow\frac{-3}{7}-x=\frac{2}{15}\Rightarrow x=\frac{-3}{7}-\frac{2}{15}\Rightarrow x=\frac{-59}{105}\)

c) \(x-\frac{1}{5}=\frac{2}{7}.\frac{-11}{5}\Rightarrow x-\frac{1}{5}=\frac{-22}{35}\Rightarrow x=\frac{-22}{35}+\frac{1}{5}\Rightarrow x=\frac{-3}{7}\)

d) \(\frac{x}{182}=\frac{-6}{14}.\frac{35}{91}\Rightarrow\frac{x}{182}=\frac{-15}{91}\Rightarrow x=\frac{\left(-15\right).182}{91}\Rightarrow x=-30\)

Bài 1 :

a, \(2^x+2^{x+1}=24\)

\(\Rightarrow2^x.1+2^x.2=24\)

\(\Rightarrow2^x\left(1+2\right)=24\)

\(\Rightarrow2^x=24\div3\)

\(\Rightarrow2^x=8=2^3\)

Vậy : x = 3

b, \(x^2-x=0\)

\(\Rightarrow x.x-x.1=0\)

\(\Rightarrow x\left(x-1\right)=0\)

Để : \(x\left(x-1\right)=0\Rightarrow x-1=0\)

\(\Rightarrow x=1\)

Vậy x = 1

Bài 2 :

a, \(Q=3+3^3+3^5+...+3^{101}\)

\(\Rightarrow9Q=3^3+3^5+3^7+...+3^{103}\)

\(\Rightarrow9Q-Q=\left(3^3+3^5+3^7+...+3^{103}\right)-\left(3+3^3+3^5+...+3^{101}\right)\)

\(\Rightarrow8Q=3^{103}-3\)

\(\Rightarrow Q=\frac{3^{103}-3}{8}\)

b, \(Q=3+3^3+3^5+...+3^{101}\)

\(\Rightarrow Q=\left(3+3^3+3^5\right)+\left(3^7+3^9+3^{11}\right)+...+\left(3^{97}+3^{99}+3^{101}\right)\)

\(\Rightarrow Q=\left(3+3^3+3^5\right)+3^6\left(3+3^3+3^5\right)+...+3^{96}\left(3+3^3+3^5\right)\)

\(\Rightarrow Q=1.273+3^6.273+...+3^{96}.273\)

\(\Rightarrow Q=\left(1+3^6+...+3^{96}\right)273\)

Vì : \(1+3^6+...+3^{96}\in N\) ; \(273=3.91\Rightarrow Q⋮91\)

Vậy ...

Phương An

soyeon_Tiểubàng giải

Võ Đông Anh Tuấn

Nguyễn Huy Tú

Trương Hồng Hạnh

Nguyễn Đình Dũng

Nguyễn Huy Thắng

Trần Quỳnh Mai

Nguyễn Thanh Vân

Nguyễn Thị Thu An

Hoàng Lê Bảo Ngọc

Silver bullet

Nguyễn Anh Duy

Lê Nguyên Hạo

Nguyễn Phương HÀ

\(a,\left|x-11\right|+x-11=0\)

\(\Rightarrow\left|x-11\right|=11-x\)

\(\Rightarrow\orbr{\begin{cases}x-11=11-x\\x-11=x-11\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=11\\x...\left(dbl>:\right)\end{cases}}\)

các bạn giúp mình với!!

a)

111=37.3

91=13.7

=> x={4,5,6}

111 = 37.3

91 = 13.7

=> x = { 4 , 5 , 6 }

1)

\(\frac{7.8^3-5.2^{10}}{\left(-16\right)^2}\)       

=  \(\frac{7.2^8.2-5.2^8.2^2}{16^2}\)

=  \(\frac{2^8.\left(2.7-5.2^2\right)}{2^8}\)

=   \(\frac{2^8.\left(-6\right)}{2^8}\)

=   \(-6\)

2)

b)\(\frac{-28}{4}\le x\le\frac{-21}{7}\)

\(\Rightarrow-7\le x\le-3\)

\(\Rightarrow x=\left\{-7;-6;-5;-4;-3\right\}\)

\(\left(\frac{11}{1.12}+\frac{11}{12.23}+\frac{11}{23.34}+....+\frac{11}{89.100}\right).x=\frac{1}{100}\)

\(\left(1-\frac{1}{12}+\frac{1}{12}-\frac{1}{23}+.....+\frac{1}{98}-\frac{1}{100}\right)x=\frac{1}{100}\)

\(\left(1-\frac{1}{100}\right).x=\frac{1}{100}\)

\(\frac{99}{100}x=\frac{1}{100}\)

\(x=\frac{1}{100}:\frac{99}{100}\)

\(x=\frac{1}{99}\)

Ta có : 10 ^ 28 = 10 ..... 0 ( 28 chữ số 0 ) chia hết cho 8​

8 chia hết cho 8

Nên 10 ^ 28 + 8 chia hết cho 8

Ta có : 10 ^ 28 + 8 = 99....9 ( 28 chữ số 9 ) + 1 + 8

=> 10 ^ 28 + 8 = 99....9 ( 28 chữ số 9 ) + 9 chia hết cho 9

Vì ƯCLN ( 8,9 ) = 1

Nên 10 ^ 28 + 8 chia hết cho 72