Question

sa se afle x daca 4ˣ + 4¹⁻ˣ = 4

Answer 1

Explicație pas cu pas:

${4}^{x} + {4}^{1 - x} = 4 \\ {4}^{x} + 4({4}^{ - x}) = 4 \\ {4}^{x} + 4({4}^{x})^{ - 1} = 4 \\ notăm: {4}^{x} = u \\ u + \frac{4}{u} = 4 < = > u + \frac{4}{u} - 4 = 0 \\ \frac{ {u}^{2} - 4u + 4 }{u} = 0 \\ \frac{(u - 2)^{2} }{u} = 0 = > u = 2 \\ {4}^{x} = 2 < = > {2}^{2x} = {2}^{1} \\ 2x = 1 = > x = \frac{1}{2}$