Let's called this number x and sum it with 35
x+35
We know this sum is equal to 100, let's equal it.
x+35=100
x+35
We know this sum is equal to 100, let's equal it.
x+35=100
Solve for x, please
1 answer:
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We're minimizing 
subject to 
. Using Lagrange multipliers, we have the Lagrangian
with partial derivatives
Set each partial derivative equal to 0:
Subtracting the second equation from the first, we find
Similarly, we can determine that
and 
by taking any two of the first three equations. So if 
determines a critical point, then
So the smallest value for the sum of squares is
when 
.
with partial derivatives
Set each partial derivative equal to 0:
Subtracting the second equation from the first, we find
Similarly, we can determine that
So the smallest value for the sum of squares is