Theory of Equations 1 Question 47

48. Find the set of all solutions of the equation

2|y||2y11|=2y1+1

(1997 C, 3M)

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Solution:

  1. Given, 2|y||2y11|=2y1+1

Case I When y(,0]

2y+(2y11)=2y1+12y=2y=1(,0]

Case II When y(0,1]

2y+(2y11)=2y1+12y=2y=1(0,1]

Case III When y(1,)

2y2y1+1=2y1+12y22y1=02y2y=0 true for all y>1

From Eqs. (i), (ii) and (iii), we get

y1[1,)



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