Question

Решыть уравнение (x+1)(x+2)(x+3)=60

Answer 1

$(x + 1)(x + 2)(x + 3) = 60 \\ \\ {x}^{3} + 3 {x}^{2} + {3x}^{2} + 9x + 2x + 6 = 60 \\ \\ {x}^{3} + 6 {x}^{2} + 11x + 6 = 60 \\ \\ {x}^{3} - 2 {x}^{2} + 8 {x}^{2} - 16x + 27x - 54 = 0 \\ \\ {x}^{2} (x - 2) + 8x(x - 2) + 27(x - 2) = 0 \\ \\ (x - 2)(x ^{2} + 8x + 27) = 0 \\ \\ x - 2 = 0 \\ \\ x = 2.$

Ответ: 2.