Triangle Inequality: (Bangladesh Online Math Camp)
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- Posts:8
- Joined:Wed Sep 28, 2011 12:24 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????
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????
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- Posts:8
- Joined:Wed Sep 28, 2011 12:24 pm
Re: Triangle Inequality: (Bangladesh Online Math Camp)
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????
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????
Re: Triangle Inequality: (Bangladesh Online Math Camp)
Something wrong with the equations..! Can't understand them properly..! There is showing some boxes of square!!
Re: Triangle Inequality: (Bangladesh Online Math Camp)
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
Re: Triangle Inequality: (Bangladesh Online Math Camp)
Please guys, try using LaTex...
It's really hard to check out these equations... They look really messed up!! :-s
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
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
Re: Triangle Inequality: (Bangladesh Online Math Camp)
Problem with Exercise 1.5 (i)..Please explain it.
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- Posts:8
- Joined:Wed Sep 28, 2011 12:24 pm
Re: Triangle Inequality: (Bangladesh Online Math Camp)
x^2 + y^2 + 2xy grter or equal 2 zero. That is the prob.
Re: Triangle Inequality: (Bangladesh Online Math Camp)
Rashique, I tried it like this...
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
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
Re: Triangle Inequality: (Bangladesh Online Math Camp)
Try reading about "the absolute value of a number" carefully!TOWFIQUL wrote:Problem with Exercise 1.5 (i)..Please explain it.
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
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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- Posts:8
- Joined:Wed Sep 28, 2011 12:24 pm
Re: Triangle Inequality: (Bangladesh Online Math Camp)
If y < 0 , is this ok? U can multiply with y iff y>0. (Mayb)