If 2 4 = 2 + 2 , then which one of the following is a possible value of ( + ) ?

Step-by-step solution

The given equation is 2 4 = 2 + 2 We know that + = + = 1 = 2 2 Substituting = 2 , we get 2 + 2 = 2 4 The equation becomes 2 4 = 2 4 1 4 = 1 4 4 = 4 4 = ( 2 - 4 ) The general solution is 4 = 2n ( 2 - 4 ) where n is an integer. Taking the positive sign, we get: 4 = 2n + 2 - 4 4( + ) = 2n + 2 + = n 2 + 8 For n = 0 , a possible value is + = 8 Answer: 8