[a,b,c],[(1)x^(2)-7x+5=0]

Prove that det[[a,b+c,a^(2)b,c+a,b^(2)c,a+b,c^(2)]]=-(a+b+c)xx(a-b)(b-c)(c-a)

Prove the identities: |[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]| =(a+b-c)(b+c-a)(c+a-b)

|[a-b, b-c, c-a], [b-c, c-a, a-b], [c-a, a-b, b-c]|=?

Evaluate the following: |[a-b, b-c, c-a],[b-c, c-a, a-b],[c-a, a-b, b-c]|

Prove that|[b+c,a,b],[c+a,c,a],[a+b,b,c]|=(a+b+c)(a-c)^2

Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a b-c^2b c-a^2c a-b^2]|=|[a, b, c],[ b ,c ,a],[ c, a ,b]|^2 .

Prove that |[a,b-c,c+b],[a+c,b,c-a],[a-b,a+b,c]|=(a+b+c)(a^2+b^2+c^2)

Prove that: |[a+b, b+c, c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]|=2|[a,b,c],[b,c,a],[c,a,b]|

If |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k|(a,b,c),(b,c,a),(c,a,b)| then k=