If (a+b+c)/(3)=(a+b)/(2)`, then c=

Verify (a + b + c) (a ^(2) +b ^(2) + c ^(2) - ab - b c - ca) = a ^(3) + b ^(2) + c ^(2) - 3 abc

|(3, a+b+c, a^(2)+b^(2)+c^(2)),(a+b+c, a^(2)+b^(2)+c^(2), a^(3)+b^(3)+c^(3)), (a^(2)+b^(2)+c^(2),a^(3)+b^(3)+c^(3), a^(4)+b^(4) +c^(4))| =K(a-b)^(2)(b-c)^(2)(c-a)^(2) then k =

If b/(a + b) = (3a - c - b)/(2b + c -a) = (-a+3c)/(2a - b + 3c) ( "where " a + b + c ne 0) , then prove that a = b = c .

If (a+b+2c+3d)(a-b-2c+3d)=(a-b+2c-3d)(a+b-2c-3d) , then 2b c is equal to 3/2 (b) (3a)/(2d) (c) 3a d (d) a^2d^2

If a= 25, b= 15, c= - 10 then (a^(3) + b^(3) + c^(3) - 3abc)/((a-b)^(2) + (b-c)^(2) + (c-a)^(2))