If `a + 2b + c= 0`, then show that: `a^(3) + 8b^(3) + c^(3)= 6abc`

If a+ b + c = 0 , show that : a^(3) + b^(3) + c^(3)= 3abc

If 3a + 5b + 4c= 0 , show that: 27a^(3) + 125b^(3) + 64 c^(3) = 180 abc

If a - 2b + 3c= 0 , state the value of a^(3) -8b^(3) + 27c^(3)

If a+b+c=5 and ab+bc+ca=10, then prove that a^(3)+b^(3)+c^(3)-3abc=-25 .

Suppose the that quadratic equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0 have a common root. Then show that a^(3)+b^(3)+c^(3)=3abc .

If a= .^(20)C_(0) + .^(20)C_(3) + .^(20)C_(6) + .^(20)C_(9) + "…..", b = .^(20)C_(1) + .^(20)C_(4) + .^(20)C_(7) + "……"' and c = .^(20)C_(2) + .^(20)C_(5) + .^(20)C_(8) + "…..", then Value of a^(3) + b^(3) + c^(3) - 3abc is

If a, b, c are in A.P, show that (i)a^3+b^3+6abc=8b^3 (ii) (a+2b-c)(2b+c-a)(a+c-b) =4abc

Factorise (i) a^(3)+8b^(3)+64c^(3)-24abc

If a+b+c=5 and ab+bc+ca=10 , then prove that a^3+b^3+c^3-3abc=-25 .

When a=3,b=0, c=-2 find the value of : a^(3)+b^(3)+c^(3)-3abc