(a) ` If x + y + z=0,` show that `x ^(3) + y ^(3) + z ^(3)= 3 xyz.`
(b) Show that ` (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)`

Verify that x ^(3) + y ^(3) + z ^(3) - 3xyz =1/2 (x + y + z) [(x-y)^(2) + (y-z) ^(2) + (z-x) ^(2) ]

Show that (b-c)/(r _(1))+ (c-a)/(r _(2))+(a-b)/(r _(3)) =0.

Prove that, a^(3)sin(B-C)+b^(3)sin(C-A)+c^(3)sin(A-B)=0

Verify : a^(3)+b^(3)+c^(3)-3abc=(1)/(2)(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)]

Match the following list of animals with their level of organisation. (A) (a - 2), (b - 3), (C-4), (d - 1) (B) (a - 2), (b - 4), (C-3), (d - 1) (C) (a - 4), (b - 1), (C-2), (d - 3) (D) (a - 1), (b - 4), (C-3), (d - 2)

If root(3)(a)+root(3)(b) + root(3)(c)=0 then (a+b+c)^(3)=

Suppose a, b, c, in R and abc = 1, if A = [[3a, b, c ],[b, 3c, a ],[c, a, 3b]] is such that A ^(T) A = 4 ^(1//3) I and abs(A) gt 0, the value of a^(3) + b^(3) + c^(3) is

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}