question_answer

            The number of real roots of the equation \[5+|{{2}^{x}}-1|={{2}^{x}}({{2}^{x}}-2)\]is : [JEE Main 10-4-2019 Afternoon]

A) 2                                 

B) 3

C) 4

D)                          1

Correct Answer: D

Solution :

Let \[{{2}^{x}}=t\]             \[5+|t-1|={{t}^{2}}-2t\]             \[\Rightarrow \underset{g(t)}{\mathop{|t-1|=}}\,\underset{f(t)}{\mathop{({{t}^{2}}-2t-5)}}\,\] From the graph So, number of real root is 1.