Question

已知正数ab和正数xy满足a+b=10,a/x + b/y=1,x+y的最小值是18,求a,b的值

Answer 1

令x+y=k

a/x+b/y=1

两式相乘,

得a+b+(ay)/x+(bx)/y=k

k=a+b+(bx²+ay²)/(xy)

≥a+b+2√(ab)

=10+2√(ab)

=18ab

=16 ,

所以a=2,b=8或者a=8,b=2