If (a+2) +(2 a-1) =2 a+1 , where 0 2 and a 1 , then is equal to -

Step-by-step solution

aligned & (a+2) 2 2 1+ ^2 2 +(2 a-1) (1- ^2 2 ) (1+ ^2 2 ) & =2 a+1 aligned Let 2 = t aligned & ( a +2) 2 t +(2 a -1) (1- t ^2 )=(2 a +1) (1+ t ^2 ) & 4 a t ^2-2 t ( a +2)+2=0 & t ^2- t ( 1 2 + 1 a )+ 1 2 a =0 & ( t - 1 2 ) ( t - 1 a )=0 & 2 = 1 2 or 2 = 1 a aligned If 2 = 1 2 or If 2 = 1 a aligned & = 2 1 2 1- 1 4 = 4 3 & = 2 1 a 1- 1 a^2 = 2 a a^2-1 . aligned