Question

3. Si:
$x + \frac{1}{x} = 3$
calcular:
$e = x {}^{2} + \frac{1}{x {}^{2} }$
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Answer 1

Recuerda:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

...

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

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

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

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