Question

If a,b,c are in continued proportion then show that (a+b)2/ ab = (b+c)2/ bc​

Answer 1

Answer:

a:b = b:c

a/b = b/c

adding 1 both sides,

(a+b) /b = (b+c) /c

multiply 2,

2(a+b) /b = 2(b+c) /c

cross Multiplication,

2(a+b)c = 2(b+c)a

divide abc on both sides,

2(a+b) /ab = 2(b+c) /bc