If x+ y- (x+y)= 3 2 , then

Step-by-step solution

x+ y- (x+y)= 3 2 array r 2 ( x+y 2 ) ( x-y 2 )- (2 ^2 ( x+y 2 )-1 )= 3 2 [ array l + =2 ( + 2 ) ( - 2 ) and =2 ^2 ( 2 )-1 array ] array aligned & 2 ( x+y 2 ) ( x-y 2 )-2 ^2 ( x+y 2 )= 3 2 -1 & 2 ( x+y 2 ) ( x-y 2 )-2 ^2 ( x+y 2 )= 1 2 & 4 ^2 ( x+y 2 )-4 ( x+y 2 ) ( x-y 2 )+1=0 aligned Substituting ( x+y 2 )= t , we get 4 t ^2-4 t ( x-y 2 )+1=0 As t is real, we get b^2-4 a c 0 aligned & [-4 ( x-y 2 ) ]^2-4 4 1 0 & 16 ^2 ( x-y 2 )-16 0 & ^2 ( x-y 2 ) 1 & ^2 ( x-y 2 )=1 aligned [ -1 1 , for all values of ] aligned & x