Question

Решите систему уравнений

Answer 1

$\left \{ {{{3}^{x - 2y} = \frac{1}{3} } \atop { {3}^{x} + {3}^{2y} = 4 \sqrt{3} }} \right. \\ \left \{ {{ \frac{{3}^{x }}{{3}^{ 2y}} = \frac{1}{3} } \atop { {3}^{x} + {3}^{2y} = 4 \sqrt{3} }} \right. \\ {3}^{x} = m \\ {3}^{2y} = n\\ \left \{ {{ \frac{m}{n} = \frac{1}{3} } \atop { m + n = 4 \sqrt{3} }} \right. \\ \left \{ {{n = 3m} \atop {m + 3m = 4 \sqrt{3} }} \right. \\ \left \{ {{n = 3m} \atop {m = \sqrt{3} }} \right. \\ \\ \left \{ {{n = 3 \sqrt{3} } \atop {m = \sqrt{3} }} \right. \\ \left \{ {{ {3}^{2y} = {3}^{1.5} } \atop {{3}^{x} = {3}^{0.5} }} \right. \\ \\ \left \{ {{x = \frac{3}{4} } \atop {y = \frac{1}{2} }} \right.$