\(T=\frac{\left(x^3+y^3\right)-\left(x^2+y^2\right)}{\left(x-1\right).\left(y-1\right)}=\frac{x^2.\left(x-1\right)+y^2.\left(y-1\right)}{\left(x-1\right)\left(y-1\right)}=\frac{x^2}{y-1}+\frac{y^2}{x-1}\)

\(T\ge2\sqrt{\frac{x^2}{y-1}.\frac{y^2}{x-1}}=\sqrt{\frac{x^2}{x-1}.\frac{y^2}{y-1}}\)(cô si 2 số nhé)

ta xét :\(\frac{x^2}{x-1}=\left(x+1\right)+\frac{1}{x-1}=\left(x-1\right)+\frac{1}{x-1}+2\ge2\sqrt{\left(x-1\right).\frac{1}{x-1}}+2=4\)

tương tự thì  \(\frac{y^2}{y-1}\ge4\)

\(\Rightarrow T\ge2\sqrt{4.4}=8\)

vậy \(MinT=8\)

37,5 x ( 4,7 + 5,3 )

= 37,5 x 10

= 375

cảm ơn bạn nhé

Đặt Tổng trên là A

A     = 1/1.3 + 1/3.5 + 1/5.7 + .... + 1/2005.2007

2. A = 2 . ( 1/1.3 + 1/3.5 + 1/5.7 + .... + 1/2005.2007 )

2A   =  2/1.3  +  2/3.5  +  2/5.7  + ..... + 2/2005.2007

2A   =  1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ..... + 1/2005 - 1/2007

2A   =   1  -  1/2007

2A   =    2006/2007

 A     =  2006/2007 : 2

A      =  2006/4014

- Hok Tot - 

               \(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+....+\dfrac{1}{2005\times2007}\)

=        \(\dfrac{1}{2}\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2005}-\dfrac{1}{2007}\right)\)

=        \(\dfrac{1}{2}\times\left(\dfrac{1}{1}-\dfrac{1}{2007}\right)\) 

=        \(\dfrac{1}{2}\times\dfrac{2006}{2007}\)

=              \(\dfrac{1003}{2007}\)

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