So to start off, set each number equal to a variable. (In this case, I will use x= 1st number and y= 2nd number)
Since the sum of the two numbers is K...
x+y=K
Therefore
y=K-x
And the sum of their squares is a minimum...
x^2+y^2=MINIMUM
Therefore
= x^2+(K-x)^2
So to simplify...
=2x^2+2Kx+K^2
Factor out the coefficient of 2 from the first two terms and complete the square
=2(x^2+Kx+(Kx/2)^2-(Kx/2)^2)+K^2
=2(x+(Kx/2)^2)^2-Kx^2+K^2
So the minimum value = -Kx^2+K^2
and x = -(Kx/2)^2
Hopefully that helps, but it is much easier to follow using real numbers (instead of generalizing >>>)
85
The two numbers are 9 and 13.
Not unless at least one of the numbers is zero.
The two numbers are 6 and 9
Difference between the sum of the squares and the square of the sums of n numbers?Read more:Difference_between_the_sum_of_the_squares_and_the_square_of_the_sums_of_n_numbers
Sum of squares? Product?
85
1
The sum of their squares is 10.
split 10 in two parts such that sum of their squares is 52. answer in full formula
12 and 12, whose squares will be 144 each. If either of the numbers is smaller than 12, then the other will be larger than 12 and its square will be larger than 144.
The two numbers are 9 and 13.
The two numbers are 6 and 9
Not unless at least one of the numbers is zero.
Difference between the sum of the squares and the square of the sums of n numbers?Read more:Difference_between_the_sum_of_the_squares_and_the_square_of_the_sums_of_n_numbers
The sum of the squares of the first 100 natural numbers [1..100] is 338350, while the sum of the first 100 natural numbers squared is 25502500.
There is no single number here. The two seed numbers are 5 and 6; their squares sum to 61.