Triangle Inequality: (Bangladesh Online Math Camp)

Discussion on Bangladesh National Math Camp
Rashik ctg
Posts:8
Joined:Wed Sep 28, 2011 12:24 pm
Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by Rashik ctg » Tue Oct 25, 2011 9:43 pm

1st case

x,y is ≥ o
x^2+xy+y^2≥ 0 no doubt.

2nd case
x,y ≤ 0 ,
then x^2 + y^2 ≥ 0 and xy ≥ 0
so , x^2+xy+y^2≥ 0
3rd case
now, x ≥ 0 , y ≤ 0 or y≥ 0, x ≤ 0

x^2 + y^2 ≥ 0 but can't prove the rest.

x^2+ y^2 - 2xy ≥ 0
x^2+ y^2 ≥ 2xy

i need to prove,
x^2+ y^2 ≥ xy

if x ≥ 0 , y ≤ 0 or y≥ 0 , x ≤ 0
2xy ≤ xy .
so????

Rashik ctg
Posts:8
Joined:Wed Sep 28, 2011 12:24 pm

Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by Rashik ctg » Tue Oct 25, 2011 9:46 pm

1st case

x,y is ≥ o
x^2+xy+y^2≥ 0 no doubt.

2nd case
x,y ≤ 0 ,
then x^2 + y^2 ≥ 0 and xy ≥ 0
so , x^2+xy+y^2≥ 0
3rd case
now, x ≥ 0 , y ≤ 0 or y≥ 0, x ≤ 0

x^2 + y^2 ≥ 0 but can't prove the rest.

x^2+ y^2 - 2xy ≥ 0
x^2+ y^2 ≥ 2xy

i need to prove,
x^2+ y^2 ≥ xy

if x ≥ 0 , y ≤ 0 or y≥ 0 , x ≤ 0
2xy ≤ xy .
so????

TOWFIQUL
Posts:10
Joined:Thu Dec 09, 2010 12:07 am
Location:Chittagong, Bangladesh
Contact:

Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by TOWFIQUL » Tue Oct 25, 2011 9:50 pm

Something wrong with the equations..! Can't understand them properly..! There is showing some boxes of square!!

iPavel
Posts:19
Joined:Fri Sep 23, 2011 5:21 pm

Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by iPavel » Tue Oct 25, 2011 9:57 pm

x^2-xy+y^2=x^2-2*x*(y/2)+(y/2)^2-(y/2)^2+y^2=(x-y/2)^2+(y^2-y^2/4) which is greater than or equal zero

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Labib
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Location:Dhaka, Bangladesh.

Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by Labib » Tue Oct 25, 2011 10:03 pm

Please guys, try using LaTex...
It's really hard to check out these equations... They look really messed up!! :-s
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.


"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

TOWFIQUL
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Location:Chittagong, Bangladesh
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Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by TOWFIQUL » Tue Oct 25, 2011 10:05 pm

Problem with Exercise 1.5 (i)..Please explain it.

Rashik ctg
Posts:8
Joined:Wed Sep 28, 2011 12:24 pm

Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by Rashik ctg » Tue Oct 25, 2011 10:09 pm

x^2 + y^2 + 2xy grter or equal 2 zero. That is the prob.

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Labib
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Location:Dhaka, Bangladesh.

Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by Labib » Tue Oct 25, 2011 10:11 pm

Rashique, I tried it like this...
Without loss of generality let $x\leq y$.
Then, $xy\leq y^2$.
So, $x^2-xy+y^2\geq 0$.
:ugeek:
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.


"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

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Labib
Posts:411
Joined:Thu Dec 09, 2010 10:58 pm
Location:Dhaka, Bangladesh.

Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by Labib » Tue Oct 25, 2011 10:17 pm

TOWFIQUL wrote:Problem with Exercise 1.5 (i)..Please explain it.
Try reading about "the absolute value of a number" carefully!
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.


"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

Rashik ctg
Posts:8
Joined:Wed Sep 28, 2011 12:24 pm

Re: Triangle Inequality: (Bangladesh Online Math Camp)

Unread post by Rashik ctg » Tue Oct 25, 2011 10:27 pm

If y < 0 , is this ok? U can multiply with y iff y>0. (Mayb)

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