Question

Giá trị của x+y , biết : 

\(2^x=8^{y+1}\) và  \(9^y=3^{x-9}\)( x, y \(\in\)N)

Answer 1

Ta có: 2^x = 8^y+1 => 2^x = (2³)^y+1 => 2^x = 2^3y+3 => x=3y+3

9^y = 3^x-9 => (3²)^y = 3^x-9 => 3^2y = 3^x-9 => 2y = x-9

Do x=3y+3 => 2y = 3y+3-9 => 2y=3y-6 => y=6

=> x = 3.6+3 = 18+3=21

=>x+y=21+6=27

Answer 2

Ta có :

\(2^x=8^{y+1}\Rightarrow2^x=\left(2^3\right)^{y+1}\Rightarrow2^x=2^{3y+3}\Rightarrow x=3y+3\)

\(9^y=3^{x-9}\Rightarrow\left(3^2\right)^y=3^{x-9}\Rightarrow3^{2y}=3^{x-9}\Rightarrow2y=x-9\)

Do : \(3y+3\Rightarrow2y=3y+3-9\Rightarrow2y=3y-6\Rightarrow y=6\)

\(\Rightarrow3.6+3=18+3=21\)

\(\Rightarrow x+y=21+6=27\)