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Algebra

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Joined:	19 Dec 2007
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27 Dec 2007 17:58:28 IST

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if a + b + c = 0 then a(b-c)^2 + b(c-a)^2 + c(a-b)^2 / abc = ??

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if a + b + c = 0 then a(b-c)^2 + b(c-a)^2 + c(a-b)^2 / abc = ??

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harsh _27

Blazing goIITian

Joined: 21 Apr 2007

Posts: 897

27 Dec 2007 18:25:30 IST

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a[b-c]² + b[c-a]² +c[a-b]² /abc = a{[b+c]²-4bc} + b{[c+a]²-4ca} + c{[a+b]²-4ab}/abc

                                           =a{a²-4bc} + b{b²-4ca} + c{c²-4ab}/abc

                                           =a³+b³+c³-12abc/abc

                                           =3abc-12abc/abc   [ since if a+b+c=0,a³+b³+c³=3abc]

                                           =-9abc/abc

                                           =- 9

dont u know me

Blazing goIITian

Joined: 5 Dec 2007

Posts: 704

29 Dec 2007 13:51:43 IST

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={a{b^2+c^2-2bc] +b[c^2+a^2-2ac]+c[a^2+b^2-2ab] } /abc
=ab[a+b] +ac[a+c] +bc[b+c]/abc -[6]
=-3-6=-9
simpl yaar rate me

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