If `|(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)`
`xx(x + a + b + c)^(2), x ne 0` and `a+b+cne0` then x is equal to

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]] = (a+b+c)^3

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]] = (a+b+c)^3

Show that |(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0.

Show that |(b+c,a,a^(2)),(c+a,b,b^(2)),(a+b,c,c^(2))|=(a+b+c)(a-b)(b-c)(c-a)

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2, B=b^2c+b c^2-a^2b-a b^2, and C=a^2c+a c^2-b^2c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

If a ne b, b,c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 , then abc =

Prove that |(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0

Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a b c(a+b+c)^3

If the equation (b^2 + c^2) x^2 -2 (a+b) cx + (c^2 + a^2) = 0 has equal roots, then