Question

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

Answer 1

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

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

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

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

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