Question
Solve each of the following equations using the formula:
$\sqrt{6} x^2-4 x-2 \sqrt{6}=0$
$\sqrt{6} x^2-4 x-2 \sqrt{6}=0$
✓
Answer
$\sqrt{6} x^2-4 x-2 \sqrt{6}=0$
Here $a =\sqrt{6}, b=-4$ and $c=-2 \sqrt{6}$
Then $x =\frac{-b \pm \sqrt{b}^2-4 a c}{2 a}$
$=\frac{-4(4) \pm \sqrt{\left((-4)^2-4 \sqrt{6}\right)(-2 \sqrt{6})}}{2(\sqrt{6})}$
$=\frac{4 \pm \sqrt{64}}{2 \sqrt{6}}=\frac{4 \pm 8}{2 \sqrt{6}}$
$=\frac{4+8}{2 \sqrt{6}}$ and $\frac{4-8}{2 \sqrt{6}}$
$=\frac{6}{\sqrt{6}}$ and $-\frac{2}{\sqrt{6}}=\sqrt{6}$ and $-\frac{\sqrt{6}}{3}$
Here $a =\sqrt{6}, b=-4$ and $c=-2 \sqrt{6}$
Then $x =\frac{-b \pm \sqrt{b}^2-4 a c}{2 a}$
$=\frac{-4(4) \pm \sqrt{\left((-4)^2-4 \sqrt{6}\right)(-2 \sqrt{6})}}{2(\sqrt{6})}$
$=\frac{4 \pm \sqrt{64}}{2 \sqrt{6}}=\frac{4 \pm 8}{2 \sqrt{6}}$
$=\frac{4+8}{2 \sqrt{6}}$ and $\frac{4-8}{2 \sqrt{6}}$
$=\frac{6}{\sqrt{6}}$ and $-\frac{2}{\sqrt{6}}=\sqrt{6}$ and $-\frac{\sqrt{6}}{3}$
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