Question

Si: x + x¹ = 4, calcular: x³ + x-³ ​

Answer 1

Desarrollamos

(x + x⁻¹)³ = (x³ + x⁻³) + 3 x² . x⁻¹ + 3 x . x⁻² = (x³ + x⁻³) + 3 (x + x⁻¹)

(x³ + x⁻³) = 4³ - 3 . 4 = 52

Answer 2

Respuesta:

x + x = 4

2x = 4

x = 2

${x}^{3} + {x}^{ - 3} = {2}^{3} + {2}^{ - 3} = 8 + \frac{1}{8} = \frac{65}{8}$