The number of real roots of the equation 

5+|2^{x}-1|=2^{x}(2^{x}-2) is : 

  • Option 1)

    3

  • Option 2)

    2

  • Option 3)

    4

  • Option 4)

    1

 

Answers (1)

5+|2^{x}-1|=2^{x}(2^{x}-2)

5+|2^{x}-1|=2^{2x}-2\cdot 2^{x}

Case 1: x\geq 0

=>5+2^{x}-1=2^{2x}-2\cdot 2^{x}

=>2^{2x}-2\cdot 2^{x}-2^{x}-4=0

=>(2^{x}-4)(2^{x}+1)=0

=>2^{x}-4=0

=>x=2

Case 2: x< 0

5+1-2^{x}=2^{2x}-2\cdot 2^{x}

=>6=2^{2x}- 2^{x}

LHS = +ve  &  RHS = - ve (no solution)

\therefore no. of solution = 1

option(4) will be correct answer.


Option 1)

3

Option 2)

2

Option 3)

4

Option 4)

1

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