so sánh 10^2020+1/10^2021+1 và 10^2020-11/10^2021-10
Đặt [tex]A=\frac{10^{2020}+1}{10^{2021}+1}[/tex]
[tex]\rightarrow A-1=\frac{10^{2020}+1}{10^{2021}+1}-1=\frac{10^{2020}-10^{2021}}{10^{2021}+1}[/tex]
[tex]B=\frac{10^{2020}-10}{10^{2021}-10}[/tex]
[tex]\rightarrow B-1=\frac{10^{2020}-10}{10^{2021}-10}-1=\frac{10^{2020}-10^{2021}}{10^{2021}-10 }[/tex]
Có [tex]2020<2021\rightarrow 10^{2020}<10^{2021}\rightarrow 10^{2020}-10^{2021}<0[/tex]
[tex]10^{2021}+1>10^{2020}-10[/tex]
[tex]\Rightarrow \frac{10^{2020}-10^{2021}}{10^{2021}+1}>\frac{10^{2020}-10^{2021}}{10^{2021}-10}[/tex]
hay [tex]A-1>B-1\Rightarrow A>B[/tex]
hay [tex]\frac{10^{2020}+1}{10^{2021}+1}>\frac{10^{2020}-10}{10^{2021}-10}>\frac{10^{2020}-11}{10^{2021}-10}[/tex]
Vậy [tex]\frac{10^{2020}+1}{10^{2021}+1}>\frac{10^{2020}-11}{10^{2021}-10}[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
