Question

Найди корни уравнения 3,4(x−7,8)(x−24)=0.

Answer 1

$3.4( {x}^{2} - 24x - 7.8x + 187.2) = 0 \\ 3.4( {x}^{2} - 31.8x + 187.2) = 0 \\{x}^{2} - 31.8x + 187.2 = 0 \\ d = {b}^{2} - 4ac = ( - 31.8) {}^{2} - 4 \times 1 \times 187.2 = 1011.24 - 748.8 = 262.44 \\ x1 = \frac{ - b + \sqrt{d} }{2a} = \frac{31.8 + \sqrt{262.44} }{2} = \frac{31.8 + 16.2}{2} = \frac{48}{2} = 24 \\ x2 = \frac{ - b - \sqrt{d} }{2a} = \frac{31.8 - \sqrt{262.44} }{2} = \frac{31.8 - 16.2}{2} = \frac{15.6}{2} = 7.8$

Ответ: 7.8 и 24