已知3x+2y=4+z,2x+2z=6+y,问是否存在x、y、z的正整数值,使得x+y+z_数学解答

已知3x+2y=4+z,2x+2z=6+y,问是否存在x、y、z的正整数值,使得x+y+z

人气：255 ℃　时间：2020-03-22 01:27:00

解答

假设x+y+z z=3x+2y-42x+2z=6+y ===> y=2x+2z-6=2x-6+6x+4y-8=8x-14+4y===> 3y=14-8xz=3x+2y-4 ===> 3z=9x+6y-12=9x-12+28-16x=16-7x3x+3y+3z=3x+14-8x+16-7x=30-12xx+y+z=10-4x10-4x3（成立）x=1时,3y=14-8x ===> y=...