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can anyone explain dis..???

Cool goIITian

Posted on
14 Apr 2012 11:25:28 IST
Posts: 47
14 Apr 2012 11:25:28 IST
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3
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can anyone explain dis..???
Engineering Entrance , JEE Main , BITSAT , JEE Advanced , Mathematics , Algebra , academic

if  w is a cube root of unity.. we know dat

1+w+w^2 =0

but if we apply A.M>G.M for 1,w,w^2

we get

thus we get 1+w+w^2 >3

so y des two statements contradict????

New kid on the Block

Joined: 29 Dec 2010 16:52:59 IST
Posts: 2
16 Apr 2012 16:11:17 IST
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the inequality applies to only non negative real numbers... since w is a complex number the inequality doesnt apply

Scorching goIITian

Joined: 10 Feb 2012 20:33:35 IST
Posts: 262
17 Apr 2012 19:53:53 IST
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Better you check the proof for AM-GM inequality. You can apply it here since the numbers are imaginary ...

New kid on the Block

Joined: 21 Nov 2010 13:24:15 IST
Posts: 6
17 Apr 2012 20:44:42 IST
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we get 1+w+w^2>3w

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