ADVANCED EXERCISES

(2) Solve for x. 


 (a) |x2 - 2x| = 1

 (b) |1 - 2x2| = 7
SOLUTION: 

 (a) |x2 - 2x| = 1
     
     x2 - 2x = 1                 or   x2 - 2x = -1
     x2 - 2x - 1 = 0                  x2 - 2x + 1 = 0
     (x - (1+))(x - (1-)) = 0     (x - 1)2 = 0
     x = 1+ , x =1-               x = 1


 (b) |1 - 2x2| = 7

     1 - 2x2 = 7   or   1 - 2x2 = -7
     x2 = -3            x2 = 4
     impossible         x = 2

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