\(\dfrac{2011\times1990-2011\times999}{2012\times999+1013}\)

\(=\dfrac{2011\times1990-2011}{2012+1013}=\dfrac{2011\times\left(1990-1\right)}{3025}\)

\(=\dfrac{2011\times1989}{3025}=\dfrac{3999879}{3025}=\dfrac{14545}{11}\)

làm cách thuận tiện nhất

Đặt a=2013

\(\Rightarrow M=\sqrt{1+a^2+\frac{a^2}{\left(a+1\right)^2}}+\frac{a}{a+1}\)

\(\Rightarrow M=\sqrt{\frac{\left(a+1\right)^2+a^2\left(a+1\right)^2+a^2}{\left(a+1\right)^2}}+\frac{a}{a+1}\)

\(\Rightarrow M=\sqrt{\frac{a^2+2a+1+a^4+2a^3+a^2+a^2}{\left(a+1\right)^2}}+\frac{a}{a+1}\)

\(\Rightarrow M=\sqrt{\frac{\left(a^4+2a^3+a^2\right)+2\left(a^2+a\right)+1}{\left(a+1\right)^2}}+\frac{a}{a+1}\)

\(\Rightarrow M=\sqrt{\left(\frac{a^2+a+1}{a+1}\right)^2}+\frac{a}{a+1}\)

\(\Rightarrow M=\frac{a^2+a+1+a}{a+1}\)(Bỏ trị tuyệt đối vì a=2013)

\(\Rightarrow M=\frac{a^2+2a+1}{a+1}=\frac{\left(a+1\right)^2}{a+1}=a+1=1013+1=1014\)

sai đề bạn ạ

như thế nào thì đúng thế

2013 x ( 1013 - 13 ) + 100 x ( 253 + 47 )

= 2013 x 1000 + 100 x 300

= 2 013 000 + 3 000

= 2 016 000

2013 x ( 1013 - 13 ) + 100 x ( 253 + 47 ) 

2013 x         1000     + 100 x       300

         2013000           +       300000

                            2313000

2012 x 2013 - 1013 x 2013 + 2013

= 2012 x 2013 - 1013 x 2013 + 2013 x 1

= 2013 x ( 2012 - 1013 + 1 )

= 2013 x         1000

=       2013000

a) 2012x2013-1013x2013+2013

=2013(2012-1013+1)

=2013x1000

=2013000

a) ( 100   +   1 ) 3   =   100 3   +   3 . 100 2 + 3.100 + 1 = 1030301.

b) ( 47   +   3 ) 3   =   50 3  = 125000.

c) ( 300   –   1 ) 3  = 26730899.

d) ( 1008   –   23 ) 3   =   1000 3   =   10 9 .

a: \(101^3=\left(100+1\right)^3\)

\(=100^3+3\cdot100^2\cdot1+3\cdot100\cdot1^2+1^3\)

=1000000+30000+300+1

=1030301

b: \(98^3+6\cdot98^2+12\cdot98+8\)

\(=98^3+3\cdot98^2\cdot2+3\cdot98\cdot2^2+2^3\)

\(=\left(98+2\right)^3=100^3=1000000\)

c: \(99^3=\left(100-1\right)^3\)

\(=100^3-3\cdot100^2\cdot1+3\cdot100\cdot1^2-1^3\)

=1000000-30000+300-1

=970299

d: \(13^3-9\cdot13^2+27\cdot13-27\)

\(=13^3-3\cdot13^2\cdot3+3\cdot13\cdot3^2-3^3\)

\(=\left(13-3\right)^3=10^3=1000\)