Question

这是一道数学题,求解.谢谢

如果1/a+1/b=5ab/(a+b)试求b/a+a/b的值

Answer 1

1/a+1/b=5ab/(a+b)化简为a^2+b^2=5a^2b^2-2ab
所以b/a+a/b=b^2/ab+a^2/ab=(a^2+b^2)/ab=（5a^2b^2-2ab）/ab=5ab-2

Answer 2

1/a+1/b=5ab/(a+b)
(a+b)/ab=5ab/(a+b)
(a+b)²=5a²b²
a²+b²+2ab=5a²b²
a²+b²=5ab/2
(a²+b²)/ab=5/2
b/a+a/b=5/2

Answer 3

b/a+a/b=3

1/a+1/b=5ab/(a+b)
(a+b)/ab=5ab/(a+b)
(a+b)^2/ab=5ab

b/a+a/b
=(a^2+b^2)/ab
=((a+b)^2-2ab)/ab
=(a+b)^2/ab-2ab/ab
=5ab-2