Question

si:
${x}^{2} - 4x + 1 = 0$

Halla:
${x}^{3} + {x}^{ - 3}$


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Answer 1

Respuesta:

52

Explicación paso a paso:

-> x^(-3) = 1/x³

x² - 4x + 1 = 0

(x²/x) - (4x/x) + (1/x) = 0

x - 4 + 1/x = 0 ---> (x + 1/x) = 4

Ahora:

(x + 1/x)³ = x³ + 3x + (3/x) + (1/x³)

(4)³ = x³ + 3x + (3/x) + (1/x³)

64 - 3x - (3/x) = x³ + (1/x)³

64 - 3(x + 1/x) = x³ + (1/x)³

64 - 3(4) = x³ + (1/x)³

52 = x³ + (1/x)³