1013:100=?
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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)
\(\Rightarrow M=\frac{a^2+2a+1}{a+1}=\frac{\left(a+1\right)^2}{a+1}=a+1=1013+1=1014\)
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Ta có : Q=\(\frac{1010+1011+1012}{1011+1012+1013}\)=\(\frac{1010}{1011+1012+1013}+\frac{1011}{1011+1012+1013}+\frac{1012}{1011+1012+1013}\)
Vì1010/1011>1010/1011+1012+1013
1011/1012>1011/1011+1012+1013
1012/1013>1012/1011+1012+1013
=>P>Q
\(\dfrac{2011\times1990-2011\times999}{2012\times999+1013}\)
\(=\dfrac{2011\times1990-2011}{2012+1013}=\dfrac{2011\times\left(1990-1\right)}{3025}\)
\(=\dfrac{2011\times1989}{3025}=\dfrac{3999879}{3025}=\dfrac{14545}{11}\)
A = 2011 2012 + 2012 2013 > 2011 2013 + 2012 2013 = 2011 + 2012 2013 > 2011 + 2012 2012 + 2013 = B
A = 2011 2012 + 2012 2013 > 2011 2013 + 2012 2013 = 2011 + 2012 2013 > 2011 + 2012 2012 + 2013 = B
2013 x ( 1013 - 13 ) + 100 x ( 253 + 47 )
= 2013 x 1000 + 100 x 300
= 2 013 000 + 3 000
= 2 016 000
1013 : 100 = 1,013
1,013
neu dung thi k cho mk di