Question

Va rog ajutati-ma!multumesc! Ex.4

Answer 1

 

$\displaystyle\\a=3^{33}=3^{3\times10 + 3}=\Big(3^3\Big)^{10}\times3^3 =27\times 27^{10} \\b = 5^{20} + 5^{22}=5^{20} + 5^{20+2}=5^{20}+5^{20}\times5^2=\\5^{20}(1+5^2)=\Big(5^2\Big)^{10}\times(1+25)=26\times 25^{10}\\ \\27\times 27^{10} >26\times 25^{10}\\\\\Longrightarrow~~~\boxed{3^{33} > 5^{20} + 5^{22}}\\\\\Longrightarrow~~~\boxed{a > b}$