Question

sí: x + x -¹ = √6, calcula : S = x⁴ + x-⁴​

Answer 1

Explicación paso a paso:

${x}+ \frac{1}{x} = \sqrt{6}$

elevamos al cuadrado

${(x + \frac{1}{x} )}^{2} = { \sqrt{6} }^{2}$

${x}^{2} + 2(x)( \frac{1}{x} ) + \frac{1}{ {x}^{2} } = 6$

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

elevamos nuevamente al cuadrado

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

${x}^{4} + 2 + \frac{1}{ {x}^{4} } = 16$

${x}^{4} + \frac{1}{ {x}^{4} } = 14$

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