题目

2x平方+2x+2分之1 [x+1][x+2]+4分之1
25的7次方-5的12次方能被120整除

提问时间：2020-08-11

答案

　2x^2+2x+1/2=2(x^2+x+1/4)
                       =2(x+1/2)^2
    (x+1)(x+2)+1/4=x^2+3x+2+1/4
                           =x^2+3x+9/4
                           =(x+3/2)^2
因为　25^7--5^12=25^7--25^6
                            =25^6x(25--1)
                            =25^6x24
                            =25^5x25x24
                            =25^5x5x5x24
                            =5^10x5x120
                            =5^11x120
所以　25^7--5^12能被120整除.
说明：符号“^”表示乘方.如25^7表示25的7次方.