Question

Determine o valor desta expressão:​

Answer 1

Resposta:

$\bold{-2\sqrt{6} }$

Explicação passo a passo:

$\sqrt{\frac{4}{(2-\sqrt{6} )^{2} } } -\sqrt{\frac{4}{(2+\sqrt{6} )^{2} } } \\\\\\\sqrt{\frac{2^{2} }{(2-\sqrt{6} )^{2} } } -\sqrt{\frac{2^{2} }{(2+\sqrt{6} )^{2} } } \\\\\\\sqrt{(\frac{2 }{2-\sqrt{6} })^{2} } -\sqrt{(\frac{2 }{2+\sqrt{6} })^{2} } \\\\\\\frac{2 }{2-\sqrt{6} } -\frac{2 }{2+\sqrt{6} } \\\\\\\frac{2 }{2-\sqrt{6} } \times\frac{2+\sqrt{6} }{2+\sqrt{6} } -\frac{2 }{2+\sqrt{6} } \times\frac{2-\sqrt{6} }{2-\sqrt{6} }$

$\frac{2\times(2+\sqrt{6}) }{(2-\sqrt{6})\times(2+\sqrt{6}) } -\frac{2\times(2-\sqrt{6}) }{(2+\sqrt{6})\times(2-\sqrt{6}) } \\\\\\\frac{4+2\sqrt{6} }{2^{2} - (\sqrt{6} )^{2} } -\frac{4-2\sqrt{6} }{2^{2} - (\sqrt{6} )^{2} } \\\\\\\frac{4+2\sqrt{6} }{4 - 6 } -\frac{4-2\sqrt{6} }{4 - 6 } \\\\\\\frac{4+2\sqrt{6} }{-2 } -\frac{4-2\sqrt{6} }{-2 } \\\\\\\frac{4+2\sqrt{6} -(4-2\sqrt{6}) }{-2 } \\\\\\\frac{4+2\sqrt{6} -4+2\sqrt{6} }{-2 } \\\\\\\frac{2\sqrt{6} +2\sqrt{6} }{-2 } \\\\\\\frac{4\sqrt{6} }{-2 }$

$-\frac{4\sqrt{6} }{2 } \\\\\\\bold{-2\sqrt{6}}$