Question

a/b=b/c. show that (a+b+c)(a-b+c)=a^2+b^2+c^2

Answer 1

It is given that, a/b=b/c

Or, b^2=ac (equation 1)

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

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

=a^2+ac-b^2+ca+c^2

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

=a^2+2b^2-b^2+c^2(from equation1)

=a^2+b^2+c^2

=RHS

Therefore, proved.

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