Question

Помогите решить уравнение
$\sqrt{5} * x^{2} - 4 * x - \sqrt{5} = 0$

Answer 1

$\sqrt{5} x^{2} - 4 x - \sqrt{5} = 0 \\ {x}^{2} - \frac{4}{ \sqrt{5} } x - 1 = 0 \\ {x }^{2} - \frac{4 \sqrt{5} }{5} x - 1 = 0 \\ {x }^{2} - 0.8\sqrt{5} x - 1 = 0$
имеем
${x}^{2} + px + q = 0$

$p = - 0.8 \sqrt{5} \\ q = - 1$

$D = {( \frac{p}{2} )}^{2} - q = \\ = (0.4 \sqrt{5 } )^{2} + 1 = 1.8$

$x _1,_2 = \: - \frac{p}{2} ± \sqrt{D} = \\ = 0.4 \sqrt{5} ± \sqrt{1.8} = 0.4\sqrt{5} ± \frac{3}{ \sqrt{5} } = \\ = 0.4\sqrt{5} ± 0.6 \sqrt{5}$

$x_1 = \sqrt{5} \\ x_2 = - \frac{ \sqrt{5} }{5}$