Question

Решите систему уравнений
lgx + lgy = 1 + lg2
2^x-6 * 2^y = 64

Answer 1

ОДЗ :  x > 0  ,  y > 0

$\left \{ {{lgx+lgy=1+lg2} \atop { 2^{x-6} * 2^{y}=64 }} \right.\\\\ \left \{ {{lg(xy)=lg10+lg2} \atop { 2^{x-6+y}=2 ^{6} }} \right. \\\\ \left \{ {{lg(xy)=lg20} \atop {x-6+y=6}} \right. \\\\ \left \{ {{xy=20} \atop {x+y=12}} \right.$
x₁ = 10       y₁ = 2
x₂ = 2         y₂ = 10
Ответ : (10 ; 2) ,(2 ; 10)