Question

si x²+1/x²=5 calcula x-1/x​

Answer 1

Respuesta:

$\boxed{\bold{x - \frac{1}{x} = \sqrt{3} }}$

Explicación paso a paso:

$\bold{Calcular: \: \: \: x - \frac{1}{x}}$

Eleve al cuadrado:

$\bold{\left ( x - \frac{1}{x} \right )^2 = x^2 - 2 \left (x \right ) \left(\frac{1}{x} \right ) + \left (\frac{1}{x} \right )^2}$

$\bold{\left ( x - \frac{1}{x} \right )^2 = x^2 - 2 \left ( \cancel{ \red{ \: x \: }} \right ) \left(\frac{1}{ \cancel{ \red{ \: x \: }}} \right ) +\frac{1}{ {x}^{2} } }$

$\bold{\left ( x - \frac{1}{x} \right )^2 = x^2 - 2 (1) +\frac{1}{ {x}^{2} } }$

$\bold{\left ( x - \frac{1}{x} \right )^2 = x^2 - 2 +\frac{1}{ {x}^{2} } }$

$\bold{\left ( x - \frac{1}{x} \right )^2 = \red{ x^2 +\frac{1}{ {x}^{2} } }- 2 }$

$\bold{Recordar \: \: que:} \: \: \: \: \boxed{ \bold{ x^2 +\frac{1}{ {x}^{2} } = 5}}$

$\bold{\left ( x - \frac{1}{x} \right )^2 = \red{5}- 2 }$

$\bold{\left ( x - \frac{1}{x} \right )^2 = 3 }$

$\boxed{\bold{x - \frac{1}{x} = \sqrt{3} }}$