怎样解x(x+1)(x-1)=120要过程

怎样解x(x+1)(x-1)=120要过程

由题可知,左边相乘的三个数为三个连续的自然数,而又可分解120=4x5x6,所以x=5.

x(1-1)=120
x=120

x（x+1)(x-1) = 120
x(x²-1) = 120
x³ - x = 120
x³ - x - 120 = 0
x³-125 -x+5 = 0
(x-5)(x²+5x+24) - (x-5) = 0
(x-5)(x²+5x+23) = 0
x²+5x+23 = (x+2.5)²+16.25＞0
∴x-5=0
∴x=5

x²－1²＝120
x²＝121
x＝±11