Question

Розвяжите за дыскриминантом Розв'яжіть за дискримінантом
ЭТО РЕШИТЬ А НЕ ВЫБРАТЬ ​

Answer 1

$a) \: \frac{1}{18} {x}^{2} - \frac{1}{6} x - 1 = \frac{1}{18} (x + 3)(x - 6) \\ \frac{1}{18} {x}^{2} - \frac{1}{6} x - 1 =0 \\ a = \frac{1}{18} \\ {x}^{2} - 3x - 18 = 0 \\ x_{1} + x_{2} = 3 \\ x_{1} \times x_{2} = - 18 \\ x_{1} = - 3 \: \: \: \: \: \: \: \: \: x_{2} = 6$

$b)\: - 2 {x}^{2} + 4.5x - 2.5 = - 2(x - 1)(x - 1.25)\\ - 2 {x}^{2} + 4.5x - 2.5 = 0 \\ a = - 2 \\ d = {4.5}^{2} - 4 \times ( - 2) \times ( - 2.5)= 0.25 \\ x_{1.2} = \frac{ - 4.5 \pm \sqrt{0.25} }{ 2 \times (- 2)} \\ x_{1} = 1 \: \: \: \: \: \: \: \: \: x_{2} = 1.25$

$c)\: {x}^{3} - 3 {x}^{2} + 2x = x( {x}^{2} - 3x + 2) = \\ = x(x - 1)(x - 2)\\ {x}^{2} - 3x + 2 = 0 \\ a = 1\\ x_{1} + x_{2} = 3 \\ x_{1} \times x_{2} = 2 \\ x_{1} = 1 \: \: \: \: \: \: \: \: \: x_{2} = 2$

$d)\: {x}^{2} y + 4xy - 21y = y( {x}^{2} + 4x - 21 )= \\ = y(x + 7)(x - 3)\\ {x }^{2} + 4x - 21 = 0 \\ a = 1 \\ x_{1} + x_{2} = - 4 \\ x_{1} \times x_{2} = - 21 \\ x_{1} = - 7 \: \: \: \: \: \: \: \: \: x_{2} = 3$