Question

tìm x , y thỏa mãn : 

a . 2^x + 124 = 5^y 

b . 10^x + 528 = y² 

gấp :(  hứa sẽ tick :D 

Answer 1

2⁰  + 124 = 5²

10⁰ + 528 = 23²

=> x=0, y=2

Answer 2

giải rõ dc ko ? @@

Answer 3

\(a,5^y-2^x=124\)

Do \(124\equiv-1\left(mod5\right)\)

Mà \(5^y\equiv0\left(mod5\right)\)

\(\Rightarrow2^x\equiv-1\left(mod5\right)\)

Vậy x chẵn

Với x = 2k

\(\Rightarrow5^y-2^{2k}=124\)

có \(124\equiv0\left(mod4\right)\)

\(4^k\equiv0\left(mod4\right)\)

\(\Rightarrow5^y\equiv0\left(mod4\right)\)

\(\Rightarrow y\)lẻ

\(\Rightarrow5^{2k+1}-2^{2k}=124\)

\(\Rightarrow5^{2k}-2^{2k}+5^{2k}.2^2=124\)

\(\Rightarrow\left(5^k-2^k\right)\left(5^k+2^k\right)+\left(5^k.2\right)^2=124\)