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3 May 2008 20:04:37 IST

Subject: Re:pls solve this:: if p+q+r=a+b+c=0,

Aatish (2308)

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Let D = $\begin{vmatrix} pa&qb &rc \\ qc&ra &pb \\ rb&pc &qa \end{vmatrix}$

=Opening the D with Sarru's formula....

D = pa.ra.qa + qc.pc.rc + rb.pb.qb - [ ra.rb.rc + pa.pb.pc + qa.qb.qc]

D = pqra³ + pqrc³ + pqrb³ - [ r³abc + p³abc + q³abc]

so... D = pqr [ a³ + b³ + c³ ] - abc [ p³ + q³ + r³ ]

but as we know.....if a + b + c =0 then.......a³ + b³ + c³ = 3abc

so...D = pqr [3abc] - abc[3pqr]

so...D = 0....

hope its clear.....

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