If ( )= ( ) , then ( 4 + )=

Step-by-step solution

The equation ( ) = ( ) is solved by rewriting x = ( 2 - x ) , giving ( ) = ( 2 - ) . Applying the general solution for A = B as A = n + B for integer n , we have = n + ( 2 - ) . Dividing by and rearranging yields + = n + 1 2 . Since the range of + is [- 2 , 2 ] , it follows that - 2 n + 1 2 2 . Solving the inequality gives -1.914 n 0.914 , so the integer solutions are n = -1 and n = 0 . This implies + = - 1 2 for n = -1 , and 1 2 for n = 0 . Using the identity ( 4 + ) = 1 2 ( + ) , we find ( 4 + ) = - 1 2 2 or 1 2