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Question

Find the set of all solutions of the equation 2|y||2y11|=2y1+1.

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Solution

When 2y11<0,
2y1<12y1<20y1<0y<1 (2x is a strictly increasing function)

Case 1: (y<0)
2(y)(12y1)=2y1+12(y)=2y=(1)

Case 2: (0y<1)
2y(12y1)=2y1+12y=2y=1

Case 3: (y>1)
2y(2y11)=2y1+12y=2y1+2y1=2(2y1)=2y
So, all of y>1,y Real Numbers

ie, This equation is satisfied y{(1)}[1,)

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