Question

(PUC - MG) sendo x e y reais, o valor de x + y no sistema 2^x=4^y e 25^x=25.5^y, é:

Answer 1

$2^x=4^y \mapsto2^x=2^{2y}\mapsto x=2y \\ \\ 25^x=25.5^y\mapsto 5^{2x}=5^2.5^y\mapsto 5^{2x}=5^{2+y}\mapsto2x=2+y \\ \\ \left \{ {{x=2y} \atop {2x=2+y}} \right. \\ \\ substituir~~x~~em \\ \\ 2x=2+y \\ 2(2y)=2+y \\ 4y-y=2 \\ 3y=2 \\ \\ y= \frac{2}{3} \\ \\ se~~x=2y \\ \\ x=2. \frac{2}{3} \\ \\ x= \frac{4}{3}$ 

$somando \\ \\ x+y= \\ \\ \frac{4}{3} + \frac{2}{3} = \frac{6}{3} =\fbox{ 2 }$