Question

Cho: A=(2010²⁰⁰⁹+2009²⁰⁰⁹)²⁰¹⁰

B=(2010²⁰¹⁰+2009²⁰¹⁰)²⁰⁰⁹.

So sánh A và B

Answer 1

\(A=\left(2010^{2009}+2009^{2009}\right)^{2010}\)

\(=\left(2010^{2009}+2009^{2009}\right)^{2009}\left(2010^{2009}+2009^{2009}\right)\)

\(>\left(2010^{2009}+2009^{2009}\right)^{2009}.2010^{2009}\)

\(=\left(2010.2010^{2009}+2010.2009^{2009}\right)^{2009}\)

\(>\left(2010.2010^{2009}+2009.2009^{2009}\right)^{2009}\)

\(=\left(2010^{2010}+2009^{2010}\right)^{2009}=B\)

Vậy \(A>B\)

Dạo này anh ít on lắm em có nhờ thì em kiếm kênh khác nhờ không thì phải đợi a on a mới làm được nhé

Answer 2

E có cách khác a ơi :)

Answer 3

\(\text{We Have:}\)

\(B=\left(2010^{2010}+2009^{2010}\right)^{2009}=\left(2010.2010^{2009}+2009.2009^{2009}\right)^{2009}\)

\(< \left(2010.2010^{2009}+2010.2009^{2009}\right)^{2009}\)

\(=\left[2010\left(2010^{2009}+2009^{2009}\right)\right]^{2009}=\left(2010^{2009}+2009^{2009}\right)^{2009}.2010^{2009}\)

\(< \left(2010^{2009}+2009^{2009}\right)^{2009}.\left(2010^{2009}+2009^{2009}\right)\)

\(=\left(2010^{2009}+2009^{2009}\right)^{2010}=A\Rightarrow A>B\)

\(\text{So: A is "lớn hơn" B =))}\)