\((\dfrac{3}{4}-81).(\dfrac{3^2}{5}-81).(\dfrac{3^3}{6}-81)...(\dfrac{3^{2000}}{200...">
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17 tháng 12 2023

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

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

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

=0

b: \(\dfrac{69}{157}-\left(2+\left(3+4+5^{-1}\right)^{-1}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(2+\left(3+4+\dfrac{1}{5}\right)^{-1}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(2+1:\dfrac{36}{5}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(2+\dfrac{5}{36}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(\dfrac{77}{36}\right)^{-1}\)

\(=\dfrac{69}{157}-\dfrac{36}{77}=\dfrac{-339}{12089}\)

10 tháng 12 2022

Câu 2

(a+3)(b-4)-(a-3)(b+4)=0

=>ab-4a+3b-12-ab-4a+3b+12=0

=>-8a=-6b

=>a/b=3/4

=>a/3=b/4

14 tháng 3 2017

Trong dãy số ta có một thừa số là : \(\dfrac{3^6}{9}-81=81-81=0\)

=> Giá trị của biểu thức :

\(\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\left(\dfrac{3^3}{6}-81\right)...\left(\dfrac{3^{2011}}{2014}-81\right)=0\)

31 tháng 3 2017

Bài này lúc đi thi mk ko làm đc nè... đến h mới bít kết quả ^^

7 tháng 10 2017

làm nhanh giúp mik vs

7 tháng 10 2017

b. \(\left(\dfrac{3^2}{9}.\dfrac{3^3}{81}\right)^{12}:\left(\dfrac{3^6}{81^2}\right)^{10}\)

\(=\left(1.\dfrac{1}{3}\right)^{12}:\left(\dfrac{1}{9}\right)^{10}\)

\(=\left(\dfrac{1}{3}\right)^{12}:\left(\dfrac{1}{9}\right)^{10}\)

\(=\left[\left(\dfrac{1}{3}\right)^2\right]^6:\left(\dfrac{1}{9}\right)^{10}\)

\(=\left(\dfrac{1}{9}\right)^6:\left(\dfrac{1}{9}\right)^{10}\)

\(=\left(\dfrac{1}{9}\right)^{-4}=6561\)

17 tháng 8 2017

Đặt \(A=\left(1+\dfrac{7}{9}\right)\left(1+\dfrac{7}{20}\right)\left(1+\dfrac{7}{33}\right)....\left(1+\dfrac{7}{2900}\right)\)

\(B=\left(81-\dfrac{3}{4}\right)\left(81-\dfrac{3^2}{5}\right)\left(81-\dfrac{3^3}{6}\right)....\left(81-\dfrac{3^{2014}}{2017}\right)\)

Ta có:

\(A=\left(1+\dfrac{7}{9}\right)\left(1+\dfrac{7}{20}\right)\left(1+\dfrac{7}{33}\right).....\left(1+\dfrac{7}{2900}\right)\)

\(A=\dfrac{16}{9}.\dfrac{27}{20}.\dfrac{40}{33}.....\dfrac{2907}{2900}\)

\(A=\dfrac{2.8}{1.9}.\dfrac{3.9}{2.10}.\dfrac{4.10}{3.11}.....\dfrac{51.57}{50.58}\)

\(A=\dfrac{2.3.4.5.6....56.57}{1.2.3.4.5.....57.58}=\dfrac{1}{58}\)

\(B=\left(81-\dfrac{3}{4}\right)\left(81-\dfrac{3^2}{5}\right).....\left(81-\dfrac{3^{2014}}{2017}\right)\)

Vì trong dãy số trên có một thừa số là \(\left(81-\dfrac{3^6}{9}\right)=\left(81-81\right)=0\)

\(\Rightarrow B=0\)

\(a=A+B\Rightarrow a=\dfrac{1}{58}+0=\dfrac{1}{58}\)(1)

Thay (1) vào đa thức \(f\left(x\right)=5x-29a\) ta được:

\(f\left(x\right)=5x-29.\dfrac{1}{58}=5x-\dfrac{1}{2}\)

Ta lại có:

\(f\left(x\right)=0\Leftrightarrow5x-\dfrac{1}{2}=0\Leftrightarrow x=\dfrac{1}{10}\)

Vậy nghiệm của đa thức trên là \(\dfrac{1}{10}\)

Chúc bạn học tốt!!!

17 tháng 8 2017

có lí

23 tháng 12 2017

a/ \(2016\dfrac{1}{6}:\dfrac{-2}{5}-16\dfrac{1}{6}:\dfrac{-2}{5}\)

\(=2016\dfrac{1}{6}.\dfrac{-5}{2}-16\dfrac{1}{6}.\dfrac{-5}{2}\)

\(=\dfrac{-5}{2}\left(2016\dfrac{1}{6}-16\dfrac{1}{6}\right)\)

\(=\dfrac{-5}{2}.2000\)

\(=-5000\)

b/ \(\left(\dfrac{4}{3}-\dfrac{3}{2}\right)^2-2.\left|-\dfrac{1}{9}\right|+\sqrt{\dfrac{4}{81}}\)

\(=\left(\dfrac{8}{6}-\dfrac{9}{6}\right)^2-2.\dfrac{1}{9}+\dfrac{2}{9}\)

\(=\dfrac{1}{4}-\dfrac{2}{9}+\dfrac{2}{9}\)

\(=\dfrac{1}{36}+\dfrac{2}{9}\)

\(=\dfrac{1}{4}\)

25 tháng 10 2022

a: \(=2\cdot\dfrac{5}{4}-3\cdot\dfrac{7}{6}+4\cdot\dfrac{9}{8}=\dfrac{5}{2}-\dfrac{7}{2}+\dfrac{9}{2}=\dfrac{7}{2}\)

b: \(=18-16\cdot\dfrac{1}{2}+\dfrac{1}{16}\cdot\dfrac{3}{4}\)

=10+3/64

=643/64

c: \(=\dfrac{2}{3}\cdot\dfrac{9}{4}-\dfrac{3}{4}\cdot\dfrac{8}{3}+\dfrac{7}{5}\cdot\dfrac{5}{14}=\dfrac{3}{2}-2+\dfrac{1}{2}=2-2=0\)

27 tháng 11 2022

a: \(=\left(\dfrac{1}{4}+\dfrac{3}{4}\right)\cdot\dfrac{18}{5}-\dfrac{6}{5}:\dfrac{-9}{5}+4\)

\(=\dfrac{18}{5}-\dfrac{6}{5}\cdot\dfrac{-5}{9}+4\)

\(=\dfrac{18}{5}+\dfrac{2}{3}+4\)

\(=\dfrac{124}{15}\)

b: \(=\dfrac{9}{25}\cdot\left(\dfrac{3}{5}-\dfrac{1}{5}+\dfrac{1}{2}\right)-\dfrac{3}{8}:\dfrac{9}{8}\)

\(=\dfrac{9}{25}\cdot\dfrac{4}{10}-\dfrac{1}{3}\)

\(=-\dfrac{71}{375}\)

c: \(=\dfrac{7}{10}:\dfrac{4}{5}+\dfrac{2}{9}:\dfrac{5}{9}+\dfrac{1}{8}\)

\(=\dfrac{7}{10}\cdot\dfrac{5}{4}+\dfrac{2}{5}+\dfrac{1}{8}\)

=1+2/5

=7/5

d: \(=\dfrac{3}{7}\left(19+\dfrac{1}{3}-33-\dfrac{1}{3}\right)-\dfrac{2}{7}=\dfrac{3}{7}\cdot\left(-14\right)-\dfrac{2}{7}=-6-\dfrac{2}{7}=\dfrac{-44}{7}\)

e: \(=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{-2^{11}\cdot3^{11}-2^{12}\cdot3^{12}}\)

\(=\dfrac{2^{12}\cdot3^{10}\cdot6}{-2^{11}\cdot3^{11}\left(1+2\cdot3\right)}=-\dfrac{2^{13}\cdot3^{11}}{2^{11}\cdot3^{11}\cdot7}=\dfrac{-4}{7}\)

5 tháng 12 2017

b) x/-4=-48/3x

=>x.3x=-4.(-48)

=>3x2= 192

=>x2=64

=>x=8

Vậy............

5 tháng 12 2017

\(a,1\dfrac{2}{3}x-\dfrac{1}{4}=\dfrac{5}{6}.\)

\(1\dfrac{2}{3}x=\dfrac{5}{6}+\dfrac{1}{4}.\)

\(1\dfrac{2}{3}x=\dfrac{13}{12}.\)

\(x=\dfrac{13}{12}:1\dfrac{2}{3}.\)

\(x=\dfrac{13}{20}.\)

Vậy \(x=\dfrac{13}{20}.\)

\(c,3^{2x+1}=81.\)

\(3^{2x+1}=3^4.\)

\(\Rightarrow2x+1=4.\)

\(\Rightarrow2x=5.\)

\(\Rightarrow x=\dfrac{5}{2}.\)

Vậy \(x=\dfrac{5}{2}.\)