Question

方程式求解

跪求 278X+280Y=117339.94 X.Y的解要是两位小数以内的，不是约等于的，是可以整除的解~~~

Answer 1

令x=100X,y=100Y,则278x+280y=11733994且x,y为整数
x=-y+42208+(170-2y)/278,故170-2y能被278整除
令y=85,则x=42123，故X=422.23,Y=0.85
令y=85+139=224,则x=42123-140=41983,故X=419.83,Y=2.24
令y=224+139=363,则x=41983-140=41843,故X=419.83,Y=3.63
令y=363+139=502,则x=41843-140=41703,故X=417.03,Y=5.02
..............................................................................
y=85+139t,x=42123-140t（t为整数）为通解

Answer 2

令x=100X,y=100Y,则278x+280y=11733994且x,y为整数
x=-y+42208+(170-2y)/278,故170-2y能被278整除
令y=85,则x=42123，故X=422.23,Y=0.85
令y=85+139=224,则x=42123-140=41983,故X=419.83,Y=2.24
令y=224+139=363,则x=41983-140=41843,故X=419.83,Y=3.63
令y=363+139=502,则x=41843-140=41703,故X=417.03,Y=5.02
这一道题涉及到不定方程的解法，大多是利用整除的性质。