Question 1158288: how do I figure out the largest possible product of two even integers whose sum is 22?
Answer by ikleyn(52798)   (Show Source):
You can put this solution on YOUR website! .
The closest analogue is this statement
Among rectangles with the given perimeter, the largest area has a square with the side length equal one fourth of the perimeter.
From this analogy, 22 = 11 + 11 will provide the greatest possible product
11*11 = 121.
Since they want even numbers, take 22 = 10 + 12, as the closest pair of even numbers to (11,11),
so your answer under given condition will be (10,12).
Solved.
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See the lessons
It is a classic problem on finding maximum value of a quadratic form.
This problem was solved MANY TIMES in this forum.
Therefore, I created lessons at this site, explaining the solution in all details.
The lessons are under these links
- HOW TO complete the square to find the minimum/maximum of a quadratic function
- Briefly on finding the minimum/maximum of a quadratic function
- HOW TO complete the square to find the vertex of a parabola
- Briefly on finding the vertex of a parabola
- A rectangle with a given perimeter which has the maximal area is a square
- A farmer planning to fence a rectangular garden to enclose the maximal area
Read these lessons attentively.
Consider them as your TEMPLATE.
Having these templates in front of you, solve the GIVEN problem by the same way.
Having it written one time, I do not see any reasons to re-write it again and again with each new given data set or formulation.
By the way, in these lessons, you will find many useful links to accompanied lessons.
Do not miss them.
Consider my lessons as your textbook, handbook, tutorial and (free of charge) home teacher.
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