math - How can I solve an equation with two variables where x is maximum? -
lets have equation - x^2+y^2=100 - there's more 1 solution. want make mathematica 8 give me solution (where natural numbers involved) x maximized (i.e x=10, y=0) i'm pretty new mathematica - , got confused whats going on... without diophantine explicit requierment: maximize[{x , x^2 + y^2 == 100}, {x, y}] (* -> {10, {x -> 10, y -> 0}} *) edit as can see, result 2 elements list. first element ( 10 ) value x (the function maximization performed). second element {x -> 10, y -> 0} , corresponding assignment rules variables @ max point. note here maximizing x , value 10 repeated in both elements, not case, want maximize general function of variables, , not vars themselves. in particular case, have 2 straightforward ways assign max value of x n : using first element of list: n = first@maximize[{x , x^2 + y^2 == 100}, {x, y}] or more general, using appropriate rule: n = x /. last@maximize[{x, x^2 + y^2 == 100}, {x, y}]