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6 tháng 4 2019

964 - 1 = (932 + 1)(932 - 1) = ... = (932 + 1)(916 + 1)(98 + 1)(94 + 1)(92 + 1)(9 + 1)(9 - 1) > (932 + 1)(916 + 1)(98 + 1)(94 + 1)(92​ + 1)(9 + 1)

6 tháng 4 2019

964=(932​+1).(932-1)

=(932+1)(916+1)(916-1)

=(932+1)(916+1)(98+1)(98-1)

=(932+1)(916+1)(98+1)(94+1)(94-1)

=(932+1)(916+1)(98+1)(94+1)(92+1)(92-1)

=(932+1)(916+1)(98+1)(94+1)(92+1)(9+1)(9-1)

Vì (932+1)(916+1)(98+1)(94+1)(92+1)(9+1)(9-1)>(932+1)(916+1)(98+1)(94+1)(92+1)(9+1)

=>964-1>(932+1)(916+1)(98+1)(94+1)(92+1)(9+1)

20 tháng 11 2016

chịu

5 tháng 8 2015

\(\left(1-\frac{1}{7}\right).\left(1-\frac{1}{8}\right).\left(1-\frac{1}{9}\right)......\left(1-\frac{1}{2011}\right)\)

\(=\frac{6}{7}.\frac{7}{8}.\frac{8}{9}.....\frac{2010}{2011}\)

\(=\frac{6.7.8.9.....2010}{7.8.9.10.....2011}\)

\(=\frac{6}{2011}\)

 

 

20 tháng 6 2021

Ta có A = 2018.2020 + 2019.2021

= (2020 - 2).2020 + 2019.(2019 + 2) 

= 20202 - 2.2020 + 20192 + 2.2019

= 20202 + 20192 - 2(2020 - 2019) = 20202 + 20192 - 2 = B

=> A = B

b) Ta có B = 964 - 1= (932)2 - 12 

= (932 + 1)(932 - 1) = (932 + 1)(916 + 1)(916 - 1) = (932 + 1)(916 + 1)(98 + 1)(98 - 1) 

= (932 + 1)(916 + 1)(98 + 1)(94 + 1)(94 - 1) 

= (932 + 1)(916 + 1)(98 + 1)(94 + 1)(92 + 1)(92 - 1) 

  (932 + 1)(916 + 1)(98 + 1)(94 + 1)(92 + 1).80 

mà A =   (932 + 1)(916 + 1)(98 + 1)(94 + 1)(92 + 1).10

=> A < B

20 tháng 6 2021

c) Ta có A = \(\frac{x-y}{x+y}=\frac{\left(x-y\right)\left(x+y\right)}{\left(x+y\right)^2}=\frac{x^2-y^2}{x^2+2xy+y^2}< \frac{x^2-y^2}{x^2+xy+y^2}=B\)

=> A < B

d) \(A=\frac{\left(x+y\right)^3}{x^2-y^2}=\frac{\left(x+y\right)^3}{\left(x+y\right)\left(x-y\right)}=\frac{\left(x+y\right)^2}{x-y}=\frac{x^2+2xy+y^2}{x-y}< \frac{x^2-xy+y^2}{x-y}=B\)

=> A < B

12 tháng 7 2016

a) \(85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)

\(=\left(85^2-15^2\right)+\left(75^2-25^2\right)+\left(65^2-35^2\right)+\left(55^2-45^2\right)\)

\(=\left(85-15\right)\left(85+15\right)+\left(75-25\right)\left(75+25\right)+\left(65-35\right)\left(65+35\right)+\left(55-45\right)\left(55+45\right)\)

\(=70.100+50.100+30.100+10.100\)

\(=7000+5000+3000+1000\)

\(=16000\)

12 tháng 7 2016

b) \(\frac{135^2+130.135+65^2}{135^2-65^2}\)

\(=\frac{135^2+2.60.135+65^2}{135^2-65^2}\)

\(=\frac{\left(135+65\right)^2}{\left(135-65\right)^2}\)

\(=\frac{200^2}{70^2}\) \(=\frac{200}{70}=\frac{20}{7}\)

30 tháng 7 2018

\(a,\frac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}\)

\(=\frac{\left(2^4\right)^3.3^{10}+2^3.3.5.\left(2.3\right)^9}{\left(2^2\right)^6.3^{12}+\left(2.3\right)^{11}}\)

\(=\frac{2^{12}.3^{10}+2^3.3.5.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3+1\right)}\)

\(=\frac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.7}=\frac{2.6}{3.7}=\frac{4}{7}\)