Question

Qual a solução dessa eq.
$x^{2} +(1- \sqrt{3})x- \sqrt{3} = 0$

Answer 1

$x^{2} + (1- \sqrt{3} )x - \sqrt{3}=0 \Longrightarrow \ a = 1 \ \ \ b = (1- \sqrt{3} ) \ \ \ c = -\sqrt{3} \\ \\ \Delta = b^2-4ac = 4-2 \sqrt{3} - 4 *(1)(-\sqrt{3}) = 4 + 2\sqrt{3}$$\ x= \dfrac{-b\pm \sqrt{\Delta }}{2a}$
$\ x_1= \dfrac{-b+\sqrt{\Delta }}{2a} = \dfrac{-1+ \sqrt{3} \ + \ \sqrt{4+ 2\sqrt{3} } }{2} \\ \\ \ x_2= \dfrac{-b-\sqrt{\Delta }}{2a} = \dfrac{-1+ \sqrt{3} \ - \ \sqrt{4+ 2\sqrt{3} } }{2}$ 
$x_1 = \dfrac{-1+1,732-2,732}{2} = \dfrac{-2}{2} = -1\\ \\ \\ x_2 = \dfrac{-1+1,732+2,732}{2} = \dfrac{3,464}{2} = 1,732 = \sqrt{3}$

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Obrigado pela oportunidade 
Boa sorte, bons estudos!
SSRC - 2015 
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