Ответы
Ответ дал:
0
x-1, x, x+1 и x+2 - последовательные натуральные числа
![xin N, x geq 2, \
(x-1)x(x+1)(x+2)=120, \ (x^2-1)(x^2+2x)-120=0, \ x^4+2x^3-x^2-2x-120=0, \ (x^4+x^3+10x^2)+(x^3+x^2+10x)+(-12x^2-12x-120)=0, \ x^2(x^2+x+10)+x(x^2+x+10)-12(x^2+x+10)=0, \ (x^2+x+10)(x^2+x-12)=0, \ left [ {{x^2+x+10=0,} atop {x^2+x-12=0;}} right. left [ {{D=-39 textless 0,} atop {x_1=-4notin N, x_2=3;}} right. \ x=3, \ x-1=2, x+1=4, x+2=5.](https://tex.z-dn.net/?f=xin+N%2C+x+geq+2%2C+%5C+%0A%28x-1%29x%28x%2B1%29%28x%2B2%29%3D120%2C+%5C+%28x%5E2-1%29%28x%5E2%2B2x%29-120%3D0%2C+%5C+x%5E4%2B2x%5E3-x%5E2-2x-120%3D0%2C+%5C+%28x%5E4%2Bx%5E3%2B10x%5E2%29%2B%28x%5E3%2Bx%5E2%2B10x%29%2B%28-12x%5E2-12x-120%29%3D0%2C+%5C+x%5E2%28x%5E2%2Bx%2B10%29%2Bx%28x%5E2%2Bx%2B10%29-12%28x%5E2%2Bx%2B10%29%3D0%2C+%5C+%28x%5E2%2Bx%2B10%29%28x%5E2%2Bx-12%29%3D0%2C+%5C++left+%5B+%7B%7Bx%5E2%2Bx%2B10%3D0%2C%7D+atop+%7Bx%5E2%2Bx-12%3D0%3B%7D%7D+right.+left+%5B+%7B%7BD%3D-39+textless++0%2C%7D+atop+%7Bx_1%3D-4notin+N%2C+x_2%3D3%3B%7D%7D+right.+%5C+x%3D3%2C+%5C+x-1%3D2%2C+x%2B1%3D4%2C+x%2B2%3D5. "xin N, x geq 2, \
(x-1)x(x+1)(x+2)=120, \ (x^2-1)(x^2+2x)-120=0, \ x^4+2x^3-x^2-2x-120=0, \ (x^4+x^3+10x^2)+(x^3+x^2+10x)+(-12x^2-12x-120)=0, \ x^2(x^2+x+10)+x(x^2+x+10)-12(x^2+x+10)=0, \ (x^2+x+10)(x^2+x-12)=0, \ left [ {{x^2+x+10=0,} atop {x^2+x-12=0;}} right. left [ {{D=-39 textless 0,} atop {x_1=-4notin N, x_2=3;}} right. \ x=3, \ x-1=2, x+1=4, x+2=5.")
Похожие вопросы
2 года назад
2 года назад
7 лет назад
9 лет назад
9 лет назад
10 лет назад
10 лет назад