Question

necesita una mano porfavor , muchas gracias

Answer 1

Respuesta:

369

Explicación paso a paso:

$x + {x}^{ - 1} = 7 \\ x + \frac{1}{x} = 7 \\ {(x + \frac{1}{x})}^{2} = {(7)}^{2} \\ {x}^{2} + 2x \frac{1}{x} + \frac{1}{ {x}^{2} } = 49 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 49 - 2 = 47 \\ {x}^{2} + {x}^{ - 2} = 47$

Luego:

$x + {x}^{ - 1} = 7 \\ x + \frac{1}{x} = 7 \\ {(x + \frac{1}{x})}^{3} = {(7)}^{3} \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3x \frac{1}{x}(x + \frac{1}{x}) =343 \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3(7) = 343 \\ {x}^{3} + \frac{1}{ {x}^{3} } = 343 - 21 = 322 \\ {x}^{3} + {x}^{ - 3} = 322$

Por tanto:

P = 47 + 322 = 369