Question

Prove that both roots of equation :(x-a)(x-b) +(x-b)(x -c)+ (x-c)(x -a)=0are equal if a= b =c.

Answer 1

Step-by-step explanation:

Let the condition be a=b=c=k

(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0

(x-k)²+(x-k)²+(x-k)²=0

3(x-k)²=0

(x-k)(x-k)=0

x=k and x=k

The roots of the equation becomes equal if a=b=c

Hence proved