Question

Решить уравнение (х+5)(х-1)(х+4)х=176 и найти сумму корней уравнения

Answer 1

$(x + 5)(x - 1)(x + 4) x = 176 \\ ( {x}^{2} + 5x - x -5)( {x}^{2} + 4x) = 176 \\ ( {x}^{2} + 4x - 5)( {x}^{2} + 4x) = 176 \\ {x}^{2} + 4x = t \\ (t - 5)t = 176 \\ {t}^{2} - 5t - 176 = 0 \\ d = {b}^{2} - 4ac = 25 - 4 \times ( - 176) = 729 = {27}^{2} \\ t1 = \frac{5 + 27}{2} = \frac{32}{2} = 16 \\ t2 = \frac{5 - 27}{2} = \frac{ - 22}{2} = - 11 \\ 1) {x}^{2} + 4x = 16 \\ {x}^{2} + 4x - 16 = 0 \\ d = {b}^{2} - 4ac = 16 - 4 \times ( - 16) = 16 + 64 = 80 \\ x1 = \frac{ - 4 + \sqrt{80} }{2} = \frac{ - 4 + 4 \sqrt{5} }{2} = - 2 + 2 \sqrt{5} \\ x2 = - 2 - \sqrt{5} \\ 2) {x}^{2} + 4x = - 11 \\ {x}^{2} + 4x + 11 = 0 \\ d = {b}^{2} - 4ac = 16 - 4 \times 11 < 0. \: \: \: = net \: kornei$
ответ: -2 +- sqrt(5).