Question

[Yến Nguyễn]

Cho A = \(\frac{10^{11}-1}{10^{12}-1}\)và B = \(\frac{10^{11}+1}{10^{12}+1}\)

So sán A và B 

Answer 1

[Nguyễn Hoàng Anh Phong]

ta có: \(A=\frac{10^{11}-1}{10^{12}-1}\Rightarrow10A=\frac{10^{12}-10}{10^{12}-1}=\frac{10^{12}-1-9}{10^{12}-1}=1-\frac{9}{10^{12}-1}.\)

\(B=\frac{10^{11}+1}{10^{12}+1}\Rightarrow10B=\frac{10^{12}+10}{10^{12}+1}=\frac{10^{12}+1+9}{10^{12}+1}=1+\frac{9}{10^{12}+1}\)

\(\Rightarrow1-\frac{9}{10^{12}-1}< 1+\frac{9}{10^{12}+1}\Rightarrow10A< 10B\Rightarrow A< B\)

Answer 2

[shitbo]

10A=10¹²-10/10¹²-1

=1-9/10¹²-1

10B=10¹²+10/10¹²+1

=1+9/10¹²+1

suy ra A<B