The sum of two numbers is 25 and their product is a maximum what are the two numbers?

Question

anonymous · Answer

i would say $12.5$

raden · Answer

yeah, they are be fifty - fifty
a= 25/2
b = 25/2
those are the  numbers

anonymous · Answer

Could you explain yourself sat?

anonymous · Answer

An answer without an explanation doesnt really excite me a little

anonymous · Answer

there are many explanations
the one i like best is by symmetry
if you call one number $x$ and the other one $y$ with $x+y=25$  then you cannot tell $x$ and $y$ apart, i.e. $x+y=y+x$ 
since they are indistinguishable, it is impossible that one can be different from the other

a most math teachery method it so call one $x$ and the other one $25-x$ and then maximize the product $x(25-x)=25x-x^2$ max occurs at the vertex, $-\frac{b}{2a}$ namely $\frac{25}{2}$

same result is achieved via calculus