Question

If x,y and z are in continued proportion,prove that (x+y)2/(y+z)2=x/z.

Answer 1

If a ,b ,c are in continued proportion then a/b = b/c i.e a:b::b:c then b²=ac

Here a = x

b =y

c = z
We can take y² = xz

Taking L .H. S ,

( x + y )² / ( y + z ) ²

= x²+ y²+2xy / y²+z²+2zy

= x²+xz+2xy / xz+z²+2zy

= x(x+z+2y)/ z(x+2y+z)

= x/z = R.H.S .

Hence Proved !^^

Answer 2

Step-by-step explanation:

If a ,b ,c are in continued proportion then a/b = b/c i.e a:b::b:c then b²=ac

Here a = x

b =y

c = z

We can take y² = xz

Taking L .H. S ,

( x + y )² / ( y + z ) ²

= x²+ y²+2xy / y²+z²+2zy

= x²+xz+2xy / xz+z²+2zy

= x(x+z+2y)/ z(x+2y+z)

= x/z = R.H.S .

Hence Proved

Hope it helps you :)