If the points, `((a^(3))/(a-1),(a^(2)-3)/(a-1)), ((b^(3))/(b-1),(b^(2)-3)/(b-1))` and `((c^(3))/(c-1)(c^(2)-3)/(c-1))` are collinear for three distinct values a, b, c and `a ne 1, b ne 1` and `c ne 1`, then show that `abc-(bc+ca+ab)+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),(c^2-3)/(c-1)) are collinear for 3 distinct values a,b,c and a!=1, b!=1, c!=1 , then find the value of abc-(ab+bc+ca)+3(a+b+c) .

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 are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)<1/2(a+b+c)

If the points A(-1,-4),B(b,c)and C(5,-1) are collinear and 3b + c = 4, find the values of b and c.

If a,b,c are real, a ne 0, b ne 0, c ne 0 and a+b + c ne 0 and 1/a + 1/b + 1/c = 1/(a+b+c) , then (a+b) (b+c)(c+a) =

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

The value of |(a,a^(2) - bc,1),(b,b^(2) - ca,1),(c,c^(2) - ab,1)| , is

If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]| =0, show that abc(ab+bc+ac) = a+b+c

If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]| =0, show that abc(ab+bc+ac) = a+b+c