" Value of "|[1,1,1],[a,b,c],[a^(3),b^(3),c^(3)]|=

By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^3,b^3,c^3]| = (a-b)(b-c)(c-a)(a+b+c)

Prove that |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=(a-b)(b-c)(c-a)(a+b+c)

Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b-c)(c-a)(a+b+c)

Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a-b)(a+b+c)

Prove that |{:(1, 1, 1),(a, b, c),(a^(3), b^(3), c^(3)):}|=(a-b)(b-c)(c-a)(a+b+c)

If a,b,are distinct,show that [[1,1,1a,b,ca^(3),b^(3),c^(3)]]=(b-c)*(c-a)*(a-b)(a+b+c)

" if " |{:(1,,1,,1),(a,,b,,c),(bc,,ca,,ab):}|=|{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(3),,c^(3)):}| where a,b,c are distinct positive reals then the possible values of abc is // are

" if " |{:(1,,1,,1),(a,,b,,c),(bc,,ca,,ab):}|=|{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(3),,c^(3)):}| where a,b,c are distinct positive reals then the possible values of abc is // are

" if " |{:(1,,1,,1),(a,,b,,c),(bc,,ca,,ab):}|=|{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(3),,c^(3)):}| where a,b,c are distinct positive reals then the possible values of abc is // are

1,1,1a,b,ca^(3),b^(3),c^(3)]|=(a-b)(b-c)(c-a)(a+b+c)