[latex]3^{2x} -3^{x} = 702[/latex] [latex]3^{2x+5} = 3^{x+2} + 2[/latex] [latex]4(9^{x}-4^{x})=13(6^{x}-4^{x})[/latex]

Решение 1)  3^(2x) - 3^x - 702 = 0 3^x = t, t > 0 t² - t - 702 = 0 D = 1 + 4*1*702 =2809 t₁ = (1 - 53)/2 t₁ = - 26 не удовлетворяет условию  t > 0 t₂ = (1 + 53)/2 t₂ = 27  3^x = 27 3^x = 3³ x = 3 Ответ: х = 3 2)  3⁵ * (3^2x) - 3² * (3^x) - 2 = 0 243 * (3^2x) - 9 * (3^x) - 2 = 0 3^x = z, z > 0 243z² - 9z - 2 = 0 D = 81 + 4*243*2 = 2025 z₁ = (9 - 45)/486 z₁ = - 36/486 не удовлетворяет условию z > 0 z₂ = (9 + 45)/486 z₂ = 54/486 z₂ = 1/9 3^x = 1/9 3^x = 3⁻² x = - 2 Ответ: х = - 2 3)  4[(3^2x) - 4^x] = 13(2^x*3^x - 4^x)  4*(3^2x) - 4*(4^x) - 13*(2^x*3^x) + 13*(4^x) = 0   4*(3^x)²  - 13*(2^x*3^x) + 9*(2^x)² = 0 делим  на (2^x)² 4*(3/2)^(2x) - 13*(3/2)^(x) + 9 = 0 (3/2)^x = y 4y² - 13y + 9 = 0 D = 169 - 4*4*9 = 25 y₁ = (13 - 5)/8 y₁ = 1 y₂ = (13 + 5)/8 y₂ = 18/8 y₂ = 9/4 (3/2)^x = 1 (3/2)^x = (3/2)⁰ x₁ = 0 (3/2)^x = 9/4 (3/2)^x = (3/2)² x₂ = 2 Ответ: x₁ = 0 ; x₂ = 2