A few days ago

Help on math homework.?

Let M and N be nonnegative real numbers. Suppose that | x + y | <= M and |xy| <= N. Determine the maximum possible value of x as a function of M and N.

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A few days ago

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1 plot it

you will be able to see and understand the problem.

| x + y | <= M will provide you with an endless \ from top left to bottom right and two parallel lines first trough (0,M) (M,0) second (-M,0), (0,-M) |xy| <= N. will cut the legs of the \ The Maximum of x will be at the point where the line that goes through (0,-M) and (M,0) y=M-x and -xy=N cross each other. -x(M-x)=N x(x-M)=N x^2-xM-N=0 x=(M+(M^2+4N)^.5)/2