Question

So sánh

\(3^{300}+4^{300}\)và\(3.24^{100}\)

Answer 1

Lớn hơn nhé !

Answer 2

Ta có :

\(3.24^{100}=3.3^{100}.8^{100}=3^{101}.8^{100}\)

Xét : \(4^{300}\)và \(3^{101}.8^{100}\)ta có : 

\(4^{300}=2^{300}.2^{300}=\left(2^2\right)^{150}.\left(2^3\right)^{100}=\)\(4^{150}.8^{100}\)

Vì \(8^{100}=8^{100}\)và \(4^{150}>3^{101}\Rightarrow4^{300}>3^{101}.8^{100}\)

\(\Rightarrow4^{300}+3^{400}>3.24^{100}\)