Question

so sánh:

M=10^30+1/10^31+1 và N=10^31+1/10^32+1

Answer 1

\(M=\frac{10^{30}+1}{10^{31}+1}\)

\(\Rightarrow10M=\frac{10\cdot(10^{30}+1)}{10^{31}+1}\)

\(\Rightarrow10M=\frac{10^{31}+10}{10^{31}+1}\)

\(\Rightarrow10M=\frac{10^{31}+1+9}{10^{31}+1}\)

\(\Rightarrow10M=1+\frac{9}{10^{31}+1}\)

\(N=\frac{10^{31}+1}{10^{32}+1}\)

\(\Rightarrow10N=\frac{10\cdot(10^{31}+1)}{10^{32}+1}\)

\(\Rightarrow10N=\frac{10^{32}+10}{10^{32}+1}\)

\(\Rightarrow10N=\frac{10^{32}+1+9}{10^{32}+1}\)

\(\Rightarrow10N=1+\frac{9}{10^{32}+1}\)

Mà\(1+\frac{9}{10^{31}+1}>1+\frac{9}{10^{32}+1}\)

Nên \(10M>10N\)

Hay \(M>N\)