A +2 2 ~A + 3 ~A is equal to which of the following? 1. 4 2 ~A ^2 ( ~A 2 ) 2. 2 2 ~A ( ~A 2 + A 2 )^2 3. 8 ~A ~A ^2 ( ~A 2 ) Select the correct answer using the code given below:

Step-by-step solution

Let A =30^ aligned & A +2 2 ~A + 3 ~A = 30^ +2 60^ + 90^ & 1 2 + 2 3 2 +1= 2 3 +3 2 & ( 2 ^2 ~A =1+ 2 ~A ) aligned Now, 4 2 ~A ^2 ( ~A 2 )=2 2 ~A [1+ A ]=2 60^ [1+ 30^ ]= 2 3 +3 2 Also, 2 ~A =2 ~A ~A & ^2 ~A + ^2 ~A =1 aligned & 2 2 ~A [ ~A 2 + A 2 ]^2 & =2 2 ~A [ ^2 ~A 2 + ^2 ~A 2 +2 ~A 2 ~A 2 ] & =2 2 ~A [1+ A ]=2 60^ [1+ 30^ ] & = 3 3 2 aligned aligned & & 8 A A ^2 ( ~A 2 ) & =4 ~A ~A [1+ A ] & =4 30^ 30^ [1+ 30^ ] & = 2 3 +3 2 aligned