Question

12. If a, b, c are in G. P., show that

(a2- b2)(b2 + c2) = (b2 - c2)(a2+ b2)​

Answer 1

Answer:

we know that if x,y,z are in G.P then y

2

=xz

⇒(ab+bc)

2

=(a

2

+b

2

)(b

2

+c

2

)

⇒a

2

b

2

+b

2

c

2

+2ab

2

c=a

2

b

2

+a

2

c

2

+b

2

c

2

+b

4

⇒b

4

+a

2

c

2

−2ab

2

c=0

⇒(b

2

−ac)

2

=0

⇒b

2

=ac