Question

If a(b-c)x² + b(c-a)x + c(a-b) is a perfect square, then a,b,c are in?
(i) A.P (ii) G.P (iii) H.P (iv) A.G.P​

Answer 1

Answer:

Correct option is

C

H.P

Since, a(b−c)x2+b(c−a)xy+c(a−b)y2 is a perfect square.

Therefore the roots of a(b−c)x2+b(c−a)xy+c(a−b)y2=0 are equal.

∴D=[b(c−a)]2−4ac(b−c)(a−b)=0

⇒b2(c−a)2=−4ac[b2−b(a+c)+ac]

⇒b2[(c−a)2+4ac]−4abc(a+c)+4a2c2=0

⇒b2(c+a)2−4abc(a+c)+4a2c2=0

⇒[b(a+c)−2ac]2=0

⇒b(a+c)=2ac

⇒b=a+c2ac