Question

Determine o valor de X:

5ˣ⁺¹+5ˣ+5ˣ⁻¹=775

Answer 1

${5}^{x + 1} + {5}^{x} + {5}^{x - 1} = 775 \\ {5}^{x} \times {5}^{1} + {5}^{x} + {5}^{x} \times {5}^{ - 1} = 775 \\ {5}^{x} (5 + 1 + {5}^{ - 1} ) = 775 \\ {5}^{x} (6 + \frac{1}{5} ) = 775 \\ {5}^{x} ( \frac{30}{5} + \frac{1}{5} ) = 775 \\ {5}^{x} \times \frac{31}{5} = 775 \\ {5}^{x} = 775 \times \frac{5}{31} \\ {5}^{x} = \frac{3875}{31} \\ {5}^{x} = 125 \\ {5}^{x} = {5}^{3} \\ x = 3$



S = {3}