Name: Paul Servic
Level: Secondary
Teacher

One of my students asked me this question and for some reason i am having a difficult time with it.

Maximize Q = xy ² where x and y are positive integers such that x + y ² = 4

The requirement that x and y be positive integers satisfying x + y ² = 4 is very restrictive. Since x is positive and y ² is also positive, the condition x + y ² = 4 implies that x is less than or equal to 3. That is x can only have the values 1, 2 or 3.

• If x = 1 then y ² = 3 and y is not an integer.
• If x = 2 then y ² = 2 and y is not an integer.
• If x = 3 then y ² = 1 and y = 1.

Thus the only positive integers x and y that satisfy x + y ² = 4 are x = 3 and y = 1.