Question

Cho A=10 mũ 2004 + 1/10 mũ 2005 +1

       B=10 mũ 2005 +1/10 mũ 2006 + 1

So sánh A và B. 

Answer 1

⇔10A=102005+110(102004+1)​

⇒10�=102005+10102005+1⇒10A=102005+1102005+10​

10�=102005+1+9102005+1=102005+1102005+1+9102005+110A=102005+1102005+1+9​=102005+1102005+1​+102005+19​

10�=1+9102005+110A=1+102005+19​

tương tự như trên ta có :

10�=1+9102006+110B=1+102006+19​

ta thấy:102005+1<102006+1

⇒9102005+1>9102006+1⇒102005+19​>102006+19​

⇒1+9102005+1>1+9102006+1⇒1+102005+19​>1+102006+19​

=>10A>10B

=>A>B