Question

解方程组x/a+y/b=1,x/b+y/a=1那种方法简便

Answer 1

x/a+y/b=1.1

x/b+y/a=1.2

1式+2式得

x(1/a+1/b)+y(1/a+1/b)=2

x+y=2/(1/a+1/b).3

1式-2式得

x(1/a-1/b)+y(1/b-1/a)=0

x(1/a-1/b)-y(1/a-1/b)=0

x-y=0

x=y.4

将4式代入3式

2x=2/(1/a+1/b)

x=1/(1/a+1/b)

x=1/[(a+b)/ab]

x=ab/(a+b)

所以x=y=ab/(a+b)