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If a, b, c are positive and unequal, sho...

If a, b, c are positive and unequal, show that value of the determinant `Delta=|(a,b,c),(b,c,a),(c,a,b)|` is negative

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`Delta = |[a,b,c],[b,c,a],[c,a,b]|`
Applying `C_1->C_1+C_2+C_3`
`Delta = |[a+b+c,b,c],[a+b+c,c,a],[a+b+c,a,b]|`
`Delta = (a+b+c) |[1,b,c],[1,c,a],[1,a,b]|`
Applying `R_2->R_2-R_1` and `R_3->R_3-R_1`
`Delta = (a+b+c)|[1,b,c],[0,c-b,a-c],[0,a-b,b-c]|`
`Delta = (a+b+c) [1((c-b)(b-c)-(a-b)(a-c))-0+0]`
`Delta = -(a+b+c)[(b-c)^2+a^2-ab-ac+bc]`
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