Question

if a/b=b/c, show that (a+b+c)(a-b-c)= a square +b square + c square

Answer 1

Step-by-step explanation:

a/b=b/c

or, b^2=ac

Now,

(a+b+c)(a-b-c)

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

=a^2-ab-ac+ba-b^2-bc+ca-cb-c^2

=a^2-ab-b^2+ba-b^2-bc+b^2-cb-c^2

=a^2-ab-b^2+ba-bc-cb-c^2

=a^2-b^2-c^2