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Word Problems/Quadratic Function

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Expert: Abe Mantell - 6/8/2009


Question
Find two numbers whose sum is 30,such that the sum of their squares is a maximum.

Answer
Let x=one of the numbers, then 30-x is the other.

The sum of the squares will then be: x^2 + (30-x)^2
Which is x^2 + 900 - 60x + x^2 = 2x^2 - 60x + 900

The trouble now is that there is no maximum!  Do the numbers need to
both be positive?  Or perhaps the question really is looking for the
sum to be a minimum?

Abe

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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