Question

Помогите решить 2 и 3
Ответ к 2 :
(2;3)
Ответ к 3 :
(3;1)

Answer 1

1. $left { {{5^x-3^{y-1}=16} atop {5^{x-1}+3^y=32}} right. \ left { {{5^x-3^{y-1}=16} atop { frac{5^x}{5}=32-3^y }} right. \ left { {{5^x-3^{y-1}=16} atop {5^x=160-15*3^{y-1}}} right. \ left { {{160-15*3^{y-1}-3^{y-1}=16} atop {5^x=160-15*3^{y-1}}} right. \ left { {{10 - 3^{y-1}=1} atop {5^x=160-15*3^{y-1}}} right. \ left { {{3^{y-1}=3^2} atop {5^x=160-15*3^{y-1}}} right. \ left { {{y-1=2} atop {5^x=160-15*3^{y-1}}} right.$
$left { {{y=3} atop {5^x=160-15*3^2} right. \ left { {{y=3} atop {5^x=160-135}} right. \ left { {{y=3} atop {5^x=5^2}} right. \ left { {{y=3} atop {x=2}} right.$

Ответ: (2;3)

2. $left { {{2^x-2^y=6} atop {2^{x+y}=16}} right. \ left { {{2^x = 6+2^y} atop {2^x*2^y=16}} right. \ left { {{2^x=6+2^y} atop {(6+2^y)2^y=16}} right. \ left { {{2^x=6+2^y} atop {(2^y)^2+6*2^y-16=0}} right. \ (2^y)^2+6*2^y-16=0 \ D=36+64=100 \ 2^y= frac{-6+10}{2} =2 \ y=1 \ left { {{2^x=6+2^1} atop {y=1}} right. \ left { {{2^x=8} atop {y=1}} right. \ left { {{2^x=2^3} atop {y=1}} right. \ left { {{x=3} atop {y=1}} right.$

Ответ: (3;1)