Matematické Fórum

stuart clark · 02. 11. 2011 08:50

Find Minimum value of $\sqrt{x^2+4}+\sqrt{(y-14)^2+1}+\sqrt{(y-x)^2+4}$

PS:: I have Got the distance between $(0,0)$ and $(14,3)$

but answer given is distance between $(0,0)$ and $(14,5)$

Why my answer is wrong.

explanation please.

thanks

musixx · 02. 11. 2011 10:13 — Editoval musixx (02. 11. 2011 10:46)

Probably, I do not understand the task but wolframalpha returns even something else, as well...

stuart clark

Using Mikiwashki Inequality

Autor skryl část textu. Zobrazit/skrýt!

P.S :: but still confusion How can We solve using Geometrically

stuart clark · 03. 11. 2011 19:36

find Min. value of $\sqrt{x^2+4}+\sqrt{(y-x)^2+4}+\sqrt{(y-14)^2+1}$

and answer is Given as

but my doubt is that why we can not take point $C(14,3)$ instead of $C(14,5)$

because When We take $C(14,3).$ Then Minimum is $=\sqrt{205}$

but here answer is $=\sqrt{221}$

explanation required

check_drummer · 03. 11. 2011 21:02

↑ stuart clark:
You cannot use (14,3) because you have to reach point with y coordinate equal to 4 - especially point (y,4). But line (0,0) - (14,3) doesn't have point with y coordinate equal to 4.

Another question is why instead of (y,4) we cannot use (y.0) - then we don't get line as optimal solution but maybe that obtained line segments (0,0)-(x,2)-(y,0)-(14,1) can be shorter for some x,y...(?)

check_drummer · 04. 11. 2011 17:42

check_drummer napsal(a):
↑ stuart clark:
Another question is why instead of (y,4) we cannot use (y.0) - then we don't get line as optimal solution but maybe that obtained line segments (0,0)-(x,2)-(y,0)-(14,1) can be shorter for some x,y...(?)

By using mirroring we can deduce that this way we will not obtain shorter segments.

Matematické Fórum

#1 02. 11. 2011 08:50

Minimum value of expression

#2 02. 11. 2011 10:13 — Editoval musixx (02. 11. 2011 10:46)

Re: Minimum value of expression

#3 03. 11. 2011 16:34 — Editoval stuart clark (03. 11. 2011 16:38)

Re: Minimum value of expression

#4 03. 11. 2011 19:36

Re: Minimum value of expression

#5 03. 11. 2011 21:02

Re: Minimum value of expression

#6 04. 11. 2011 17:42

Re: Minimum value of expression

check_drummer napsal(a):

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