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Express =|2b c-a^2c^2b^2c^2 2c a-b^2a^2b...

Express `=|2b c-a^2c^2b^2c^2 2c a-b^2a^2b 62a^2 2a b-c^2|` as square of a determinant of hence evaluate if.

Text Solution

Verified by Experts

The correct Answer is:
`[3abc-a^(2)-b^(3)-c^(3)]^(2)`
The given determinants is
`|{:(a,, b,,c),(b,,c,,a),(c,,a,,b):}| xx |{:(-a,,c,,b),(-b,,a,,c),(-c,,b,,a):}|=Delta `[row by row multiplication]
Therefore
`Delta = |{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}||{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}|=|{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}|^(2)`
`=[a(bc-a^(2))+b(ac-b^(2))+c(ab-c)^(2))]^(2)`
`=[3abc -a^(3)-b^(3)-c^(3)]^(2)`
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