SOLUTION: hi, could you please give me the equations/solutions for these questions, thanks, 1. the sum of two number is 20. what is the least possible sum of their squares? 2. what num

Question 159195: hi,
could you please give me the equations/solutions for these questions,
thanks,
1. the sum of two number is 20. what is the least possible sum of their squares?
2. what number exceeds its square by the greatest amount?
i will be waiting.
thank you
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1. the sum of two number is 20. what is the least possible sum of their squares?
2. what number exceeds its square by the greatest amount?
--------------
1. S = x^2 + (20-x)^2
S = x^2 + 400 -40x +x^2
S = 2x^2 - 40x + 400
Set 1st derivative = 0
4x - 40 = 0
x = 10
10^2 + 10^2 = 200
--------------
2. D = x-x^2
Set 1st derivative = 0
1-2x = 0
x = 1/2

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