Question

Помогите, пожалуйста: $3^{x-1} + 3^{x} + 3^{x+1} = 13*3^{x^{2}-7 }$

Answer 1

${3}^{x - 1} + {3}^{x} + {3}^{x + 1} = 13 \times {3}^{ {x}^{2} - 7} \\ {3}^{x} ( \frac{1}{3} + 1 + 3) = 13 \times {3}^{ {x}^{2} - 7 } \\ {3}^{x} \times \frac{13}{3} = 13 \times {3}^{ {x}^{2} - 7} \\ 13 \times {3}^{x - 1} = 13 \times {3}^{ {x}^{2} - 7} \\ {3}^{x - 1} = {3}^{ {x}^{2} - 7} \\ x - 1 = {x}^{2} - 7 \\ {x}^{2} - x - 6 = 0 \\ \\ x_{1}= - 2 \\ x_{2} = 3$


ОТВЕТ: -2 ; 3.