Comparing with quadratic equation
Ax²+Bx+C=0
A=(b-c),B=c-a,C=a-b
When roots are equal ,its discriminant will be zero,means√( b^2-4ac)=0 i.e
b^2-4ac=0
Discriminate when roots are equal
D=B²-4AC=0
D=(c-a)²−4(b-c)(a-b)=0
D=(c²+a²−2ac)-4(ba-ac-b²+bc)=0
D=c²+a²−2ac-4ab+4ac+4b²-4bc=0
c²+a²+2ac-4b(a+c)+4b²=0
(a+c)²-4b(a+c)+4b²=0
[(a+c)-2b]²=0
a+c=2b
LIKE IF SATISFIED