Đáp án:
a) $\rm A>B$
b) $\rm C<D$
Giải thích các bước giải:
a)
`A=(10^8+1)/(10^9+1)`
`to 10A=(10^9+10)/(10^9+1)=(10^9+1+9)/(10^9+1)=1+9/(10^9+1)`
`B=(10^9+1)/(10^10+1)`
`to 10A=(10^10+10)/(10^10+1)=(10^10+1+9)/(10^10+1)=1+9/(10^10+1)`
Vì : `10^9<10^10 to 10^9+1<10^10+1`
`to 9/(10^9+1)>9/(10^10+1)`
`to 1+9/(10^9+1)>1+9/(10^10+1)`
hay `10A>10B`
$\rm \to \ A>B$
b)
`C=(5^12+1)/(5^13+1)`
`5C=(5^13+5)/(5^13+1)=(5^13+1+4)/(5^13+1)=1+4/(5^13+1)`
`D=(5^11+1)/(5^12+1)`
`5D=(5^12+5)/(5^12+1)=(5^12+1+4)/(5^12+1)=1+4/(5^12+1)`
Vì : `5^13>5^2 to 5^13+1>5^12+1`
`to 4/(5^13+1)<4/(5^12+1)`
`to 1+4/(5^13+1)<1+4/(5^12+1)`
hay `5C<5D`
`to C<D`
