If the points `((a^3)/((a-1))),(((a^2-3))/((a-1))),((b^3)/(b-1)),(((b^2-3)/((b-1))),` and `(((c^2-3))/((c-1))),` where `a , b , c` are different from 1, lie on the `l x+m y+n=0` , then `a+b+c=-m/l` `a b+b c+c a=n/l` `a b c=((m+n))/l` `a b c-(b c+c a+a b)+3(a+b+c)=0`

If the points ((a^3)/((a-1))),(((a^2-3))/((a-1))),((b^3)/(b-1)),((b^2-3)/((b-1))) , ((c^3)/(c-1)) and (((c^2-3))/((c-1))), where a , b , c are different from 1, lie on the l x+m y+n=0 , then (a) a+b+c=-m/l (b) a b+b c+c a=n/l (c) a b c=((m+n))/l (d) a b c-(b c+c a+a b)+3(a+b+c)=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

If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]|=0, show that a b c(a b+b c+c a)=a+b+c

Show that: ((3^a)/(3^b))^(a+b)\ ((3^b)/(3^c))^(b+c)\ ((3^c)/(3^a))^(c+a)=1

If a,b,c are distinct real numbers and |{:(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(2),c^(3)-1):}|=0 then

Let ABC be a triangle inscribed in a circle and let l_(a)=(m_(a))/(M_(a)), l_(b)=(m_(b))/(M_(b)), l_(c )=(m_(c ))/(M_(c )) where m_(a), m_(b), m_(c ) are the lengths of the angle bisectors of angles A, B and C respectively , internal to the triangle and M_(a), M_(b) and M_(c ) are the lengths of these internal angle bisectors extended until they meet the circumcircle. Q. The maximum value of the product (l_(a)l_(b)l_(c))xxcos^(2)((B-C)/(2)) xx cos^(2)(C-A)/(2)) xx cos^(2)((A-B)/(2)) is equal to :

If a b c = 0, then ({(x^a)^b}^c)/({(x^b)^c}^a) = (a)3 (b) 0 (c) -1 (d) 1

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+c) where a, b, c are all different, then the determinant |(1,1,1),((x-a)^(2),(x -b)^(2),(x -c)^(2)),((x -b) (x -c),(x -c) (x -a),(x -a) (x -b))| vanishes when

If |b+c c+a a+b a+b b+c c+a c+a a+b b+c|=k|ab c c a b b c a| , then value of k is 1 b. 2 c. 3 d. 4

If a^(1/3)+\ b^(1/3)+\ c^(1/3)=0 , then+? (a) a+b+c=0 (b) (a+b+c)^3=27\ a b c (c) a+b+c=3a b c (d) a^3+b^3+c^3=0