The sum of the squares of two positive numbers is 200 their minimum product is

Solution：Let the two numbers be x and yThen,as the question says, x�0�5+y�0�5=200，x>0，y>0It represents a part of the circle x�0�5+y�0�5=(10√2)�0�5 which is in the first quadrant.Suppose that hyperbola xy=k and the part of the circle intersect.Through drawing the graph we can see that the unknown positive number k can be infinitely small.That is， the minimum product value of x and y does not exist.

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