Question

$\left \{ {{2^{x}*3^{y}=12} \atop{2^{y}*3^{x}=18 }} \right.$
Решить систему через дискриминант

Answer 1

2^x * 3^y = 12

2^y * 3^x = 18

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2^x * 3^y = 2^2*3

2^y * 3^x = 2 * 3^2

x = 2  y = 1

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или делим первое на второе

2^x * 3^y / 2^y * 3^x = 12 / 18

(2/3)^x*(3/2)^y = 2/3

(2/3)^(x-y) = 2/3

x - y = 1

умножаем первое на второе

2^x * 3^y *2^y * 3^x = 12 * 18

2^(x + y)*3^(x + y) = 6^3

6^(x + y) = 6^3

x + y = 3

x = 2

y = 1