Question

已知x,y∈R,a＞1,b＞1,若a^x=b^y=2,a+√b=4,则2/x+1/y的最大值

Answer 1

a^x=2

a=2^(1/X)

b^y=2

b=2^(1/y)

a+√b=2^(1/x)+2^(1/(2y))=4

所以4=2^(1/x)+2^(1/(2y))≥2√2^(1/x+1/(2y))

2^(1/x+1/(2y))≤2^2

所以1/x+1/(2y)≤2

所以2/x+1/y≤4