Question

Ayudenme porfaa, con resolucion!

Answer 1

Recuerda este artificio en productos notables:

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

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Divide todo entre x^2:

$4( \frac{ {x}^{4} }{ {x}^{2} } + \frac{1}{ {x}^{2} } ) = \frac{ {5x}^{2} }{ {x}^{2} } \\ 4( {x}^{2} + \frac{1}{ {x}^{2} } ) = 5 \\ {x}^{2} + \frac{1}{ {x}^{2} } = \frac{5}{4} \\ {x}^{2} + 2 + \frac{1}{ {x}^{2} } = \frac{5}{4} + 2 \\ {x}^{2} + 2(x) (\frac{1}{x} ) + \frac{1}{ {x}^{2} } = \frac{5 + 8}{4} \\ {(x + \frac{1}{x} )}^{2} = \frac{13}{4}$