Home
Class 12
MATHS
Prove that |{:(1, 1, 1),(a, b, c),(a^(3)...

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

Text Solution

AI Generated Solution

To prove that \[ | \begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^3 & b^3 & c^3 \end{vmatrix} | = (a-b)(b-c)(c-a)(a+b+c) ...
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

Using the property of determinants and without expanding prove that abs([1,1,1],[a,b,c],[a^3,b^3,c^3])=(a-b)(b-c)(c-a)(a+b+c)

The value of the determinant /_\=|(1,1,1),(a,b,c),(a^3,b^3,c^3)| is (A) (a-b)(b-c)(c-a)(a+b+c) (B) abc(a+b)(b+C)(c+a) (C) (a-b)(b-c)(c-a) (D) none of these

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)

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

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

Prove that :(a+b+c)^(3)-a^(3)-b^(3)-c^(3)=3(a+b)(b+c)(c+a)

Prove that (a+b+c)^(3)-a^(3)-b^(3)-c^(3)=3(a+b)(b+c)(c+a) .

Show that det[[1,1,1a^(2),b^(2),c^(2)a^(3),b^(3),c^(3)]]=(b-c)(c-a)(a-b)(bc+ca+ab)det[[a^(2),b^(2),c^(2)a^(3),b^(3),c^(3)]]=(b-c)(c-a)(a-b)(bc+ca+ab)det[[a^(2),b^(2),c^(2)a^(3),b^(3),c^(3)]]=(b-c)(c-a)(a-b)(bc+ca+ab)