Q35 of 110 Page 260

Prove that = - (a – b) (b – c) (c – a) (a2 + b2 + c2).

Operating R1→R1-R2, R2→R2-R3




Taking (a-b), (b-c) common from R1, R2 respectively



Operating R1→R1- R2




Taking (a-c) common from R1



Expanding with C1


= (a-c)(a-b)(b-c)×(2b2+2bc+2c2-ab-b2-bc-ac-bc-c2+a2+ab+ac)


=-(c-a)(b-c)(a-b)(a2+b2+c2)


Hence Proved


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