Question

plz solve this sum in full method with right answer

Answer 1

Given,
a/b=b/c and a, b, c > 0.
To show,
i) (a+b+c) (b-c) = ab-c^2
ii) (a^2+b^2)(b^2+c^2)= (ab+bc) ^2
iii) (a^2+b^2/ab) = a+c/b
Solution,
i) LHS=(a+b+c) (b-c)
=ab-ac+b^2-bc+bc-c^2
=ab-ac+b^2-c^2
=a(b-c)+b^2-c^2
=ab-c^2
=RHS
ii)LHS= (a^2+b^2)(b^2+c^2)
Now take RHS to easy to proof LHS=RHS-
RHS=(ab+bc) ^2
=ab^2+bc^2+2* ab * bc
=a^2+b^ * b^2+c^2
=LHS
iii)LHS= (a^2+b^2/ab)
=ab
=a+c/b