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melkorthefoul
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Homework Statement
Hi guys,
I'm doing a rather long math modelling task. As part of the task, I have to investigate the following argument:
There is a rectangle ABCD. It is sliced by the line EF, such that EF is parallel to AD and BC. M is the midpoint of BC. X is a point on the line EF (the position of X, which is denoted as x, is the variable in this investigation).
If, for a given value of x, the square of the distance AX is minimized, then for this value of x the distance AX is also minimized (proved that). Then, if, for a given value of x, the square of the distance XM is minimized, then for this value of x the distance XM is also minimized (Proved that the same way). Therefore, if the sum of the squares of the distances AX and XM are minimized for a given value of x, then the sum of the distances (AX+XM) is also minimized (Need just a bit of advice here)
Homework Equations
AX2=f(x)
XM2=g(x)
AX2+XM2=h(x)
AX+XM=i(x)
The Attempt at a Solution
I've kinda proved the last bit as well, by saying that the square root of (a+b) does not equal the square root of a plus the square root of b, as the argument assumes that the square root of h(x) = i(x) . However, I just wanted to clarify something: would saying just this be enough, or do I have to prove it? And how would I go about doing that?
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