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One number exceeds another number by 18. Find the numbers if the result of adding their sum and their product is a minimum.

Respuesta :

If one number exceeds another by 18, the relation between the two numbers is

[tex]x = y+18[/tex]

So, their product is

[tex]xy = (y+18)y = y^2+18[/tex]

This parabola is concave up, so its vertex is its minimum. The vertex lies in [tex](0,18)[/tex].

So, the two numbers are 0 and 18.

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