If `a+b+c=0,\ (a+b)(b+c)(c+a)` equals (a) `a b\ (a+b)` (b) `(a+b+c)^2` (c) `-a b c` (d) `a^2+b^2+c^2`

If a+b+c=0,darr(a+b)(b+c)(c+a) equals (a) ab backslash(a+b)(b)(a+b+c)^(2)(c)-abc(d)a^(2)+b^(2)+c^(2)

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

If a+b+c=0 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) 1 (c) -1 (d) 3

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

The expression (a-b)^3+\ (b-c)^3+\ (c-a)^3 can be factorized as (a) (a-b)(b-c)(c-a) (b) 3(a-b)(b-c)(c-a) (c) -3\ (a-b)(b-c)(c-a) (d) (a+b+c)(a^2+b^2+c^2-a b-b c-c a)

Prove: |((b+c)^2, a^2, b c) ,((c+a)^2, b^2 ,c a),( (a+b)^2, c^2, a b)|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2) .

If a,b,c gt 0, then (a )/(2a + b +c ) = (b)/(a + 2b +c)= (c )/(a +b + 2c) = ?

If a , b ,c in Ra n da(a+b)+b(b+c)+c(c+a)=0 then a. a=b=c=0 b. a+b+c+=0 c. (a-b)^2+(b-c)^2+(c-a)^2=0 d. a^3+b^3+c^3+3a b c=0