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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: arithmetic progression
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[Post New]3 Jul 2008 10:46:58 IST
    Subject: arithmetic progression
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dodo (0)

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if x , y , z  are the real numbers satisfying the expression    25(9x^2+y^2) +9z^2-15(5xy+yz+3xz)=0                          


prove x , y , z   are in arithmetic progression
    
[Post New]3 Jul 2008 10:52:48 IST
    Subject: arithmetic progression
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sandeepramesh (1247)

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Rewrite it as (15x-5y)^2 + (5y-3z)^2 + (15x-3z)^2 = 0
implies 15x = 5y = 3z = k say
implies 2y = 2k/5 = k/3 + k/15 = x+z
Hence proved!
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