20 13 Jinhua No.10 middle school simulation mathematics

Solution: divide both sides of the equation by xy(xy≠0) at the same time.

1/y+4/x= 1

∴x+y=(x+y)*( 1/y+4/x)

=5+x/y+4y/x≥5+2*√(x/y)*(4y/x)

Take "=" if and only if x/y=4y/x, that is, x = 6 and y = 3.

That is, the minimum value of x+y is 9.

Comments: Looking at the substitution and mean inequality of "1", this question is slightly clever, and it needs to be divided by xy to get 1 and then calculated.

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