0
What is the minimum value of the sum of their squares if the sum of two numbers is K?
Wiki User
∙ 16y ago
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 >>>)
Wiki User
∙ 16y ago
Add your answer:
Earn +20 pts
Two numbers have a sum of thirteen what is the minimum product of the sum of their squares?
85
What are the numbers when the sum of two numbers is 22 and the sum of their squares is 250?
The two numbers are 9 and 13.
The sum of two numbers is 15 and the sum of their squares is 117 what are the two numbers?
The two numbers are 6 and 9
Is the sum of the squares of two numbers equal to the square of the sum of the numbers?
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?
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
Two numbers have a sum of 20 if their squares is a minimum find the numbers Complete the square to find the minimum?
Sum of squares? Product?
Two numbers have a sum of thirteen what is the minimum product of the sum of their squares?
85
The sum of two numbers is k Find the minimum value of the sum of their cubes?
1
The sum of two positive numbers is 4 and the sum fo their cubes is 28 What is the sum of their squares?
The sum of their squares is 10.
Explain the square of the sum of two numbers is different from the sum of the squares of two numbers?
split 10 in two parts such that sum of their squares is 52. answer in full formula
The sum of two numbers is 24 find the numbers whose squares are to be minimum?
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.
What are the numbers when the sum of two numbers is 22 and the sum of their squares is 250?
The two numbers are 9 and 13.
The sum of two numbers is 15 and the sum of their squares is 117 what are the two numbers?
The two numbers are 6 and 9
Is the sum of the squares of two numbers equal to the square of the sum of the numbers?
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?
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
What is the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum?
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.
The sum of the squares of two consecutive positive numbers is 61. What is the number?
There is no single number here. The two seed numbers are 5 and 6; their squares sum to 61.
