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Algebra

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22 Mar 2008 10:25:55 IST

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If x+y+z = 0 with x,y,z[-2,1] then prove that x²+y²+z² 6

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dont u know me

Blazing goIITian

Joined: 5 Dec 2007

Posts: 704

22 Mar 2008 12:36:38 IST

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uhooo pardesi see yaar it was asked 2 proved

2 2 2
x + y + z <=6 hence as 1/2 <6

pardesi .svk

Scorching goIITian

Joined: 7 Dec 2007

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22 Mar 2008 12:37:40 IST

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i didn't get anything there

sandeep ramesh

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22 Mar 2008 12:50:41 IST

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what was that abt?? :D :D

Hari Shankar

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22 Mar 2008 13:13:09 IST

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I think this is what pardesi and co. meant:

x+y+z = 0, means all the numbers cannot be negative or all positive (if you exclude the trivial solution (0,0,0 )

So, either any two are positive or two are negative.

Case 1: say, x and y are positive. then z can take a negative value of "utmost" -2, with x and y both equal to 1

For this case x²+y²+z²

Case 2: x, y are both negative. Then |z|

1 and |x+y| = |z|

1 Hence |x|

1 and |y|

So x²+y²+z²

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