समीकरण `5+ |2^(x)-1| =2^(x) (2^(x)-2)` के वास्तविक मुलो की संख्या है

Options

A. 4
B. 3
C. 2
D. 1

Answer

D

Explanation

`2^ x =t`

Condition 1`=``tge1`
` 5 + t- 1 = t(t-2)` `=t^ 2 -2t`
`t^2-3t-4=0`
`Rightarrowt^2-4t+t-4=0`
` t(t-4)+1(t-4)= 0`
` (t-4) (t+1 )= 0`

` t= 4,rarr2^ x =4`
`x=2`

` t=-1` [impossible because `2^xgt0`]

Condition 2`=``tlt1`
` 5 - t+ 1 = t(t-2)` `=t^ 2 -2t`
`t^2-t-6=0`
`Rightarrowt^2-3t+2t-6=0`
` t(t-3)+2(t-3)= 0`
` (t-3) (t+2)= 0`

`t=3` [ impossible because `tlt1`]

`t=-2` [impossible because `2^xgt0`]