Решение2^(2x - 2y) + 2^(x - y) = 22^(2x + 1) + (1/2)^(2y - 1) = 52^(2x - 2y) + 2^(x - y = 22^[2*(x - y)] + 2^(x - y) = 22^(x - y) = z, z > 0z² + z - 2 = 0z₁ = - 2 не удовлетворяет условию z > 0z₂ = 12^(x - y) = 12^(x - y) = 2⁰x - y = 0x = yподставим у = х во второе уравнение2^(2x + 1) + (1/2)^(2y - 1) = 52^(2x + 1) + (1/2)^(2x - 1) = 52*2^(2x) + 2*(1/2)^(2x) - 5 = 0умножим на 2^(2x)2*2^(4x) - 5*2^(2x) + 2 = 02^2x = t2t² - 5t + 2 = 0D = 25 - 4*2*2 = 9t₁ = (5 - 3)4t₁ = 1/2t₂ = (5 + 3)/4t₂ = 21) 2^2x = 1/22^2x = 2⁻¹2x = - 1x₁ = - 1/22^2x = 2¹2x = 1x₂ = 1/2так как x = y, то y₁ = - 1/2y₂ = 1/2Ответ: (- 1/2; - 1/2) (1/2 ; 1/2)