Question

a=?
b=?

Va rog frumos ajutați-mă!

Answer 1

$\it(\underbrace{1+1+1+ ...\ +1}_{\ de\ a\ \ ori})\cdot a^b+8a^{b+1}=3^6 \Rightarrow 1\cdot a\cdot a^b+8a^{b+1}=3^{2\cdot3} \Rightarrow \\ \\ \\ \Rightarrow a^{b+1}+8a^{b+1}=(3^2)^3 \Rightarrow a^{b+1}(1+8)=9^3 \Rightarrow a^{b+1}\cdot9=9^3|_{:9} \Rightarrow \\ \\ \\ \Rightarrow a^{b+1}=9^2=3^4=81^1\ \ \ \ \ \ \ (*)$

$\it (*) \Rightarrow (a,\ b)\in\{(9,\ 1);\ (3,\ 3);\ (81,\ 0)\}$