如果1/a+1/b=4/a+b,则分式b/a+a/b=________

如果1/a+1/b=4/a+b,则分式b/a+a/b=________
如果1/a+1/b=4/a+b,则分式b/a+a/b=________

如果1/a+1/b=4/a+b,则分式b/a+a/b=________
1/a+1/b
=(a+b)/ab=4/(a+b)
(a+b)²=4ab
a²+b²+2ab=4ab
所以a²+b²=2ab
所以b/a+a/b
=(a²+b²)/ab
=2ab/ab
=2

1/a+1/b=4/a+b
(a+b)(1/a +1/b)=4
1+b/a + a/b +1 =4
b/a+a/b=4-1-1=2

化简第一式，得(a+b)/ab=4/(a+b) => (a+b)方=4ab => (a-b)方=0 => a=b，所以b/a+a/b=2

1/a+1/b=4/a+b
两边同乘a+b
a+b（1/a+1/b）=4
ab/a²+2ab+b²=4
a²+2ab+b²=4ab
a²+b²=2ab
b/a+a/b=a²+b²/ab
代入a²+b²=2ab
2ab/ab=2