If x, y, z are in continued proportion , prove
(x + y)^2/(y + 2) = x/z
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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 !^^
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