If `(a+b+c)=0` then find `(a^2+b^2+c^2)/(a^2b^2+b^2c^2+c^2a^2)`

If sinthetaand costheta are the roots of the equation ax^2+bx+c=0 , then (A) (a-c)^2=b^2+c^2 (B) (a+c)^2=b^2-c^2 (C) a^2=b^2-2ac (D) a^2+b^2-2ac=0

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

In triangle A B C ,2a csin(1/2(A-B+C)) is equal to (a) a^2+b^2-c^2 (b) c^2+a^2-b^2 (c) b^2-c^2-a^2 (d) c^2-a^2-b^2

In any A B C , the value of 2a csin((A-B+C)/2) is (a) a^2+b^2-c^2 (b) c^2+a^2-b^2 (c) b^2-c^2-a^2 (d) c^2-a^2-b^2

If a+b+c=9 and a b+b c+c a=40 , find a^2+b^2+c^2

In a triangle A B C ,\ (a^2-b^2-c^2)tanA+(a^2-b^2+c^2)tanB is equal to (a^2+b^2-c^2)tanC (b) (a^2+b^2+c^2)tanC (b^2+c^2-a^2)tanC (d) none of these

If sinalpha and cosalpha are the roots of the equation a x^2+b x+c=0 , then b^2= (a) a^2-2a c (b) a^2+2a c (c) a^2-a c (d) a^2+a c

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c ^2 (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

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^2' c-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

Divide: (a^2+2a b+b^2)-(a^2+2a c+c^2)b y\ 2a+b+c