Question

If
then
a, b, c are in continued proportion
prove that (a+b+c) (b-c) = ab - c²​

Answer 1

Step-by-step explanation:

a:b:c

a×c=b^2------(1)

(a+b+c)(b-c)=ab-ac+b^2-bc+bc-c^2

= ab-ac+b^2-c^2

from (1),

=ab-b^2+b^2-c^2

=ab-c^2

hence,

(a +b +c)(b-c)=(ab-c^2)

hope it is Helpful.