Posted by **bobby** on Tuesday, December 16, 2008 at 7:52pm.

Find two numbers whose sum is 10 for which the sum of their squares is a minimum.

- Calculus -
**Reiny**, Tuesday, December 16, 2008 at 7:55pm
two numbers : x and 10-x

S = x^2 + (10-x)^2

dS/dx = 2x - 2(10-x)

= 0 for max/min

x = 5

so the numbers are both 5

- Calculus -
**Damon**, Tuesday, December 16, 2008 at 7:56pm
x and (10-x)

s = x^2 + (10-x)^2

s = x^2 + 100 -20x + x^2

s = 2 x^2 - 20 x + 100

s/2 = x^2 -10 x + 100 we can minimize half the sum easier than the whole sum

That is a parabola and you could find the vertex but since you said this was "calculus" we will take the derivative and set to zero.

0 = 2 x - 10

x = 5

10-x = 5

- Calculus -
**Damon**, Tuesday, December 16, 2008 at 8:23pm
Interesting the answer is halfway between.

Exploring that

Say a sum of two numbers is s

We want to minimize the sum of squares of x^2 and (s-x)^2

sum = 2 x^2 -2sx

d sum/dx = 0 = 4 x -2s

x = s/2

so it works for any old sum, not just 10

## Answer This Question

## Related Questions

- Math - Minimizing Sum: Find two positive numbers whose sum is 100 and the sum of...
- Calculus - find the two numbers whose sum of the squares is a minimum if the ...
- math - Find two positive numbers whose sum is 50 such that the sum of their ...
- Math - Find two numbers whose difference is 16, and the sum of whose squares a ...
- maths - Find the two numbers whose differences is 8 and the sum of their ...
- calculus - Find two positive numbers whose product is 100 and whose sum is a ...
- Pre-Calculus - If the sum of two numbers is 1 and the sum of the cubes of the ...
- Math - The sum of two numbers is five. The sum of the squares of the two numbers...
- math - Find: Two numbers whose sum -10 and whose product is 5. ;;; x+y = -10 x...
- Math - One number is 10 larger than another. Write a function in standard form ...

More Related Questions