52 Show that `a(b - c)x^2` +` b(c - a)xy` + `c(a - b)y^2` will be a perfect square if a, b, c are in H.P

Show that If a(b-c)x^(2)+b(c-a)xy+c(a-b)y^(2)=0 is a perfect square,then the quantities a,b,care in harmonic progresion

If a(b-c)x^(2)+b(c-a)x+c(a-b) is a perfect square then a,b,c are in

If the left hand side of the equation a(b-c)x^2+b(c-a) xy+c(a-b)y^2=0 is a perfect square , the value of {(log(a+c)+log(a-2b+c)^2)/log(a-c)}^2 , (a,b,cinR^+,agtc) is

Roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are real and equal, then (A) a+b+c!=0 (B) a,b,c are in H.P. (C) a,b,c are in H.P. (D) a,b,c are in G.P.

Show that |a b c a+2x b+2y c+2z x y z|=0

If the roots of equation a(b-c)x^2+b(c-a)x+c(a-b)=0 be equal prove that a,b,c are in H.P.

If a(b-c)x^(2)+b(c-a)xy+c(a-b)y^(2)=0 is a perfect square,then (log(a+c)+log(a-2b+c))/(log(a-c)) is equal to

If a, b,c be the sides foi a triangle ABC and if roots of equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal then sin^2 A/2, sin^2, B/2, sin^2 C/2 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these