If x + y = 10 what is the maximum value of xy.

[Guest]

If x + y = 10 what is the maximum value of xy.

[Guest]

[tex]x+y=10[/tex] so that means [tex]y=10-x[/tex].
Substituting this into [tex]xy[/tex] gives [tex]x(10-x) = 10x-x^2[/tex].
Using the standard method of completing the square
http://en.wikipedia.org/wiki/Completing_the_square
we see that [tex]10x-x^2 = 25-(x-5)^2[/tex].
This is obviously maximized when the square term is [tex]0[/tex] i.e. when [tex]x=5[/tex] we get the maximum value of [tex]25[/tex] for [tex]xy[/tex].

Hope this helped,

R. Baber.

[Guest]

Yes, very helpful, thank you and a good link to wiki

[palashoni]

Very usefully for me!

[leesajohnson]

The link to Wikipedia which you have shared is too useful and helpful to understand the problem.