Question

Uma equação cujas raízes são
$4 + \sqrt{6 \: }$
ou
$4 - \sqrt{6}$

$a) {x}^{2} + 8x + 10 = 0$
$b) {x}^{2} - 8x + 10 = 0$
$c) {x}^{2} + 8x - 10 = 0$
$d) {x}^{2} - 8x - 10 = 0$
$e) {x}^{2} + 10x + 8 = 0$


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Answer 1

Forma fatorada da equação do 2º grau a · (x  x') · (x - x'')

$x'=4+\sqrt{6} \ e \ x''=4-\sqrt{6} \vamos \ utilizar\ a=1\\\\a\cdot(x-x')\cdot(x-x'')=0\\\\1\cdot\big[x-\big(4+\sqrt{6}\big)]\cdot\big[x-\big(4-\sqrt{6}\bg)\big]=0\\\\\big[x-\big(4+\sqrt{6}\big)]\cdot\big[x-\big(4-\sqrt{6}\bg)\big]=0\\\\x^2-(4-\sqrt{6}\big)\cdot x-(4+\sqrt{6}\big) \cdot x+(4+\sqrt{6}\big)\cdot(4-\sqrt{6}\big)=0\\\\x^2-4x+\sqrt{6}x-4x-\sqrt{6} x+4^2-(\sqrt{6})^2=0\\\\x^2-4x-4x+\sqrt{6}x-\sqrt{6} x+16-6=0\\\\x^2-8x+10=0$