Question

$1) \: \: \: 3x {}^{2}+4x+5 = 0$
$2) \: \: \: x - \frac{1}{x} = 4.8$

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Answer 1

1)

$3 {x}^{2} + 4x + 5 = 0 \\ D = {4}^{2} - 4 \times 3 \times 5 = 16 - 60 = - 44$

Дискриминант отрицательный, поэтому корней нет.

2)

$x - \frac{1}{x} = 4.8 \: \: \: \: \: \: \: \: \: \: \: x≠0 \\ x - \frac{1}{x} = \frac{24}{5} \\ x - \frac{1}{x} - \frac{24}{5} = 0 \\ \frac{5 {x}^{2} - 5 - 24x }{5x} = 0 \\ 5 {x}^{2} - 5 - 24x = 0 \\ 5 {x }^{2} - 24x - 5 = 0 \\ 5 {x}^{2} + x - 25x - 5 = 0 \\ x(5x + 1) - 5(5x + 1) = 0 \\ (5x + 1)(x - 5) = 0 \\ \\ 5x + 1 = 0 \\ 5x = - 1 \\ x = - \frac{1 }{5} \\ x_{1} = - 0.2 \\ \\ x - 5 = 0 \\ x_{2} = 5$