Question

so sánh:

A=1990^80+3/1990^82+3

B=1990^60+3/1990^62+3

 

Answer 1

Ta có: \(1990^2\cdot A=\frac{1990^{82}+3\cdot1990^2}{1990^{82}+3}=\frac{1990^{82}+3+3\cdot\left(1990^2-1\right)}{1990^{82}+3}=1+\frac{3\cdot\left(1990^2-1\right)}{1990^{82}+3}\)

\(1990^2\cdot B=\frac{1990^{62}+3\cdot1990^2}{1990^{62}+3}=\frac{1990^{62}+3+3\left(1990^2-1\right)}{1990^{62}+3}=1+\frac{3\left(1990^2-1\right)}{1990^{62}+3}\)

Ta có: \(1990^{82}+3>1990^{62}+3\)

=>\(\frac{3\left(1990^2-1\right)}{1990^{82}+3}<\frac{3\left(1990^2-1\right)}{1990^{62}+3}\)

=>\(\frac{3\left(1990^2-1\right)}{1990^{82}+3}+1<\frac{3\left(1990^2-1\right)}{1990^{62}+3}+1\)

=>\(1990^2\cdot A<1990^2\cdot B\)

=>A<B