#Ext2 help

41 messages · Page 1 of 1 (latest)

civic fossil
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Can someone help me with part b of this question. I tried using the hint and subbing Z=x as it says to find real solutions.

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formal wave
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ah it's 4h old oops

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oh well

civic fossil
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Idk I got x is between -2 and 2 lol

formal wave
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yea right

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now can you have non-real solutions to that equation ?

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@civic fossil

civic fossil
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That’s where I’m a bit confused

formal wave
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think geometrically

civic fossil
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I think it might be an ellipse

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So in that case yes ig

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But not sure

formal wave
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a very screwed up ellipse in this case

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imagine I took a point here

image.png
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the sum of the lengths of the two solid lines is |z| + |z-2| right

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ok but |z| is already greater than 2, since x itself is greater than 2

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so x+iy can't solve the equation

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roughly the same thing if x<0, this time |z-2| is too big

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now for the more interesting case

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again will |z| + |z-2| be greater than 2 ?

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@civic fossil

civic fossil
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No?

formal wave
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why not ?

civic fossil
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Oh Lord I’m lost

civic fossil
formal wave
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you want all the z such that |z| + |z+2| <= 2 right

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that's what you're trying to solve

civic fossil
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Yep

formal wave
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and what I'm saying is that can't happen if you pick z=x+iy with x>2

civic fossil
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Ok yeah got that

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But why we are thinking that x>2 in the first place

formal wave
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because this length in green is already bigger than 2

image.png
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I'm just splitting cases

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either x is outside [0,2] or it is inside

civic fossil
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Right ok

formal wave
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the reasoning is a tiny bit different inside than outside

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outside is the easy case

formal wave