A = B chĂc là thế

\(A>B\),có lẽ là bởi vì \(A\)có mũ  ²⁰¹⁰ ;còn \(B\)thì lại có mũ ²⁰⁰⁹.

Trước tiên ta có: \(\sqrt[2009]{19^{2009}+5^{2009}}>\sqrt[2009]{19^{2009}}=19\)

và \(\sqrt[2009]{19^{2009}+5^{2009}}>\sqrt[2009]{5^{2009}}=5\)

Ta có: \(\sqrt[2009]{A}=\left(19^{2009}+5^{2009}\right)\sqrt[2009]{19^{2009}+5^{2009}}\)

\(\sqrt[2009]{B}=19^{2010}+5^{2010}\)

\(\Rightarrow\sqrt[2009]{A}-\sqrt[2009]{B}=\left(19^{2009}+5^{2009}\right)\sqrt[2009]{19^{2009}+5^{2009}}-\left(19^{2010}+5^{2010}\right)\)

\(=\left(19^{2009}.\sqrt[2009]{19^{2009}+5^{2009}}-19^{2010}\right)+\left(5^{2009}.\sqrt[2009]{19^{2009}+5^{2009}}-5^{2010}\right)\)

\(=19^{2009}\left(\sqrt[2009]{19^{2009}+5^{2009}}-19\right)+5^{2009}\left(\sqrt[2009]{19^{2009}+5^{2009}}-5\right)\)

\(>19^{2009}.\left(19-19\right)+5^{2009}.\left(5-5\right)=0\)

\(\Rightarrow\sqrt[2009]{A}>\sqrt[2009]{B}\)

\(\Rightarrow A>B\)

A= (\(\left(\frac{19^{2010}}{19}+\frac{5^{2010}}{5}\right)^{2010}\)=\(\frac{\left(5.19^{2010}+19.5^{2010}\right)^{2010}}{19^{2010}.5^{2010}}\)= A(1)/A(2)

B = \(\frac{\left(19^{2010}+5^{2010}\right)^{2010}}{19^{2010}+5^{2010}}\)= B(1)/B(2)

Ta thấy A(1) >B(1), A(2)<B(2) => A>B

ủa bạn duchinhle tại sao 19^2010.5^2010 lại lớn hơn 19^2020+5^2010