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).