;((

\(Ư\left(144\right)=\left\{1,2,3,4,6,8,9,12,16,18,24,36,48,72,144\right\}\)

\(Ư\left(324\right)=\left\{1,2,3,4,6,9,12,18,27,36,54,81,108,162,324\right\}\)

\(Ư\left(576\right)=\left\{1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576\right\}\)

\(Ư\left(1024\right)=\left\{1,2,4,8,16,32,64,128,256,512,1024\right\}\)

\(Ư\left(1296\right)=\left\{1,2,3,4,6,8,9,12,16,24,27,36,48,54,72,81,108,144,162,216,324,432,648,1296\right\}\)

\(Ư\left(2304\right)=\left\{1,2,3,4,6,8,9,12,16,18,24,32,48,64,72,96,128,144,192,256,288,384,576,768,1152,2304\right\}\)

\(Ư\left(2500\right)=\left\{1,2,4,5,10,20,25,50,100,125,250,500,625,1250,2500\right\}\)

\(Ư\left(10000\right)=\left\{1,2,4,5,8,10,16,20,25,40,80,100,125,200,250,400,500,625,1000,1250,2000,2500,5000,10000\right\}\)

\(Ư\left(48\right)=\left\{1;-1;-2;2;3;-3;6;-6;8;-8;12;-12;-24;24;16;-16;48;-48\right\}\\ Ư\left(8\right)=\left\{1;-1;2;-2;-4;4;8;8\right\}\\ Ư\left(14\right)=\left\{-1;1;2;-2;7;-7;14;-14\right\}\\ Ư\left(20\right)=\left\{-1;1;2;-2;5;-5;4;-4;-10;10;-20;20\right\}\)

a) Ư(12²) = Ư(144) = {1; 2; 3; 4; 6; 8; 9; 12; 16; 18; 24; 32; 48; 72; 144}

b) Ư(18²) = Ư(324) = {1; 2; 3; 4; 6; 9; 12; 18; 27; 36; 54; 81; 108; 162; 324}

c) Ư(24²) = Ư(576) = {1; 2; 3; 4; 6; 8; 9; 12; 16; 18; 24; 32; 36; 48; 64; 72; 96; 144; 192; 288; 576}

d) Ư(32²) = Ư(1024) = {1; 2; 4; 8; 16; 32; 64; 128; 256; 512; 1024}

Đặt \(A=\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\left(\dfrac{3^3}{6}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)

\(=\left(\dfrac{3^6}{9}-81\right)\cdot\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)

\(=\left(81-81\right)\cdot\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)

=0

theo bài ra ta có:

\(C=\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...\left(\frac{3^{2013}}{2016}-81\right)\)

C = \(\left(\frac{3}{4}-81\right)...\left(\frac{3^6}{9}-81\right)...\left(\frac{3^{2013}}{2016}-81\right)\)

\(C=\left(\frac{3}{4}-81\right)...\left(81-81\right)...\left(\frac{3^{2013}}{2016}-81\right)\)

C = \(\left(\frac{3}{4}-81\right)...0...\left(\frac{3^{2013}}{2016}-81\right)\)

C = 0

vậy C = 0

(3/4 -81 )(3^2/5 -81 )(3^3/6 -81)......(3^2000/2003 -81)

ta viết tiếp dãy số (3/4 -81 )(3^2/5 -81 )(3^3/6 -81)(3^4/7 - 81 ) (3^5/8 -81)(3^6/9 -81).........(3^2000/2003 -81) thì thấy 3^6/9=81 ->3^6/9 -81=0 -> dãy số bằng 0 -> (3/4 -81 )(3^2/5 -81 )(3^3/6 -81)......(3^2000/2003 -81) =0

Minh k hiểu cho lắm. Bạn viết theo công thức toán olm cho sẵn đi cho dễ đọc

Dễ thấy (\(\frac{3}{4}\)-81); (\(\frac{3^2}{5}\)-81); (\(\frac{3^3}{6}\)-81);... (\(\frac{3^{2007}}{2010}\)-81) có dạng (\(\frac{3^x}{3+x}\)-81) và x\(\varepsilon\){1;2;3;...2007}.

Nếu x=6 thì \(\frac{3^x}{3+x}\)-81=\(\frac{3^6}{3+6}\)-81=0

=>  (\(\frac{3}{4}\)-81) (\(\frac{3}{4}\)-81)(\(\frac{3^3}{6}\)-81)...​(\(\frac{3^6}{3+6}\)-81)...(\(\frac{3^{2007}}{2010}\)-81)=0

Mà |x-30|-6001=(\(\frac{3}{4}\)-81) (\(\frac{3}{4}\)-81)(\(\frac{3^3}{6}\)-81)...​(\(\frac{3^6}{3+6}\)-81)...(\(\frac{3^{2007}}{2010}\)-81)

=>|x-30|-6001=0

=>|x-30|=6001

=>x-30=6001 hoặc x-30=-6001

=>x=6031 hoặc x=-5971

-------------------The end----------------

\(\text{|x - 30| - 6001 = }\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...\left(\frac{3^{2007}}{2010}-81\right)\)

\(\Rightarrow\text{ |x - 30| - 6001 = }\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...\left(\frac{3^6}{9}-3^4\right)...\left(\frac{3^{2007}}{2010}-81\right)\)

\(\Rightarrow\left|x-30\right|- 6001 = \left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...\left(3^4-3^4\right)...\left(\frac{3^{2007}}{2010}-81\right)\)

\(\Rightarrow|x - 30| - 6001 = \left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...0...\left(\frac{3^{2007}}{2010}-81\right)\)

\(\Rightarrow\text{|x - 30| - 6001 = }0\)

\(\Rightarrow\left|x-30\right|=6001\) 

\(\Rightarrow x-30=6001\)hoặc \(x-30=-6001\)

\(\Rightarrow x=6031\)hoặc\(x=-5971\)

Vậy: x= 6031 hoặc x= -5971

(Nói thật thì mình mới lớp 7, đây có phải của lớp 8 không?)

\(\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)....\left(\frac{3^{2000}}{2003}-81\right)\)

\(=\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...\left(\frac{3^6}{9}-81\right)...\left(\frac{3^{2000}}{2003}-81\right)\)

\(=\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)....\left(81-81\right)...\left(\frac{3^{2000}}{2003}-81\right)\)

\(=\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)....0....\left(\frac{3^{2000}}{2003}-81\right)\)

\(=0\)