SOLUTION: Find two positive numbers x and y such that they add to 20 and x^2 + y^2 is a minimum.

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Question 1139594: Find two positive numbers x and y such that they add to 20 and x^2 + y^2 is a minimum.
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%5E2 + y%5E2 = x%5E2 + %2820-x%29%5E2 = x%5E2+%2B+400+-+40x+%2B+x%5E2 = 2x%5E2+-+40x+%2B400.


The minimum is achieved at  x = -b%2F%282a%29 = -%28-40%29%2F%282%2A2%29 = 40%2F4 = 10.


ANSWER.  x = y = 10.

Solved.

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On finding the maximum/minimum of a quadratic function see the lessons
    - 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
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.