5^x+5^y=30 x+y=3 система

Question

5^x+5^y=30
x+y=3
система

Answer 1

X = 3 - y
5^(3 - y) + 5^y = 30 *

125/5^y + 5^y - 30 = 0 
Пусть 5^y = t
125/t + t - 30 = 0 
t^2 - 30t + 125 = 0 
D = 900 - 500 = 400 
t₁ = ( 30 + 20)/2 = 25;
t₂ = ( 30 - 20)/2 = 5;

5^y = 25
y₁ = 2

5^y = 5
y₂ = 1

x₁ = 1
y₁ = 2

x₂ = 2
y₂ = 1

Ответ
( 1; 2) ; (2; 1)