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![[Post New]](/templates/default/images/icon_minipost_new.gif) 8 Dec 2007 11:07:33 IST
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If alpha ,beta gamma are yhe roots of the equation x3 + P0x2 + P1x +P2 =0
then (1-alpha2)(1-beta2)(1-gamma2) =
plz give all the steps.
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the given expression is equal to 1 +(ab)^2 +(bc)^2+(ca)^2 - (a^2 +b^2 +c^2) -(abc)^2
and use a+b+c = -Po , ab+bc+ca= P1 and abc=-P2
also use
(ab)^2 +(bc)^2+(ca)^2
= (ab+bc+ca)^2 - 2[(ab)(bc)+(bc)(ca)+(ca)(ab)]
= (ab+bc+ca)^2 - 2abc[a+b+c]
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8 Dec 2007 21:06:38 IST
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a^2 +b^2 +c^2 = (a+b+c)^2 - 2(ab+bc+ca)
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