Question

$Determinar \: el \: valor \: de \: {x}^{4} + {x}^{ - 4}$
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Answer 1

Respuesta:

47

Explicación paso a paso:

$x^{4} +x^{-4} =x^{4}+\frac{1}{x^{4} }$

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$x^{2} +3x+1=0$

$x^{2} +1=3x$

$\frac{x^{2} }{x} +\frac{1}{x} =\frac{3x}{x}$$x^{4} +x^{-4} =47$

$x+\frac{1}{x} =3$

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$(x)^{2} +(\frac{1}{x})^{2} =(3)^{2}$

$x^{2} +2(x)(\frac{1}{x} )+(\frac{1}{x})^{2} =9$

$x^{2} +2+\frac{1}{x^{2} } =9$

$x^{2} +\frac{1}{x^{2}} =7$

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

$x^{4} +2+\frac{x}{x^{4} } =49$

$x^{4} +\frac{1}{x^{4} } =47$