This looks like a Lagrange multiplier problem. Have you heard of this method?
For did you mean to square the in ?
I feel my IQ drops with every second I look at this excercise, that's why I ask you guys:
Given with that satisfy and
Find such that the distance to the origin is maximal/minimal
However, I can't find points that satisfy to both equations of
We can derive
(1)
(2)
(3)
From (2) we get
From (3) we get
Only seems ok. But it gives , ...scheisse
So, I can't find any that could possibly satisfy the equations, let alone
Can someone fix my brains? What's wrong here?
Yes, I'm familiar with the method. And the excercise itself is not my problem.
My problem is the definition of , with , from wich I derive that is empty
So I think there's a mistake in the excercise. I think indeed it must be .
But no, I didn't mean to square the , this is exactly the excercise.
Yeah, thank you both.
Needed my brain to get fixed, perhaps I wasn't thinking clear.
But the mistake I made was at (3). Somehow I thought the positive root was wich is clearly wrong.
getting the positive root of is . This gives
Hence we need to take the intersection of (1),(2) and we find
I guess, no-one really did an effort to see that I made a lame calculation error at (3). Now clearly C is not empty and consists of the points
with