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If the lvalue of the determinants |(a,1,...

If the lvalue of the determinants `|(a,1,1),(1,b,1),(1,1,c)|` is positive then:

A

`abcgt1`

B

`abcgt-8`

C

`abcgt-8`

D

`abcgt-2`

Text Solution

Verified by Experts

The correct Answer is:
2
`Deltagt0`
abc+ 2`gt`3`(abc)^(1//3)`
Let `(abc)^(1//3)`=x
`x^(3)+2gt3x`
`(x-1)^(2)(x+2)gt0`
`therefore x+2gt0`
`xgt-2`
`(abc)^(1//3)gt-2`
`abcgt-8`
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