If (x-y), x, (x+y) are three distinct numbers which are in harmonic progression and x y , then 1+ y is equal to

Step-by-step solution

(x-y), x, (x+y) are in HP. Then, x= 2 (x-y) (x+y) (x+y)+ (x-y) x= 2 x+ 2 y 2 x y x= 2 ^2 x+2 ^2 y-2 2 x y ^2 x y= ^2 x+ ^2 y-1 ^2 x( y-1)= ( ^2 y-1 ) ^2 x(1- y)= (1- ^2 y ) ^2 x (2 ^2 y 2 )= ^2 y ^2 x (2 ^2 y 2 )= (2 y 2 y 2 )^2 ^2 x (2 ^2 y 2 )=4 ^2 y 2 ^2 y 2 ^2 x= (2 ^2 y 2 -1 )+1 y+1= ^2 x or 1+ y= ^2 x