QJEEM19Ma62bf: JEE Main 2019 Mathematics - Class 11 JEEM19Ma62bf Solution: The number of real roots of the equation 5 +

When 2^x $\ge$ 1

5 + 2^x –1 = 2^x (2^x – 2)

Let 2x = t

$\Rightarrow$ 5 + t – 1 = t (t – 2)

$\Rightarrow$ t = 4, – 1(rejected)

$\Rightarrow$ 2x = 4

$\Rightarrow$ x = 2

Now when 2^x < 1

5 + 1 – 2^x = 2^x (2^x – 2)

Let 2^x = t

$\Rightarrow$ 5 + 1 – t = t (t – 2)

$\Rightarrow$ 0 = t² – t – 6

$\Rightarrow$ 0 = (t – 3) (t – 2)

$\Rightarrow$ t = 3, – 2

2^x = 3, 2^x = – 2 (rejected)

$\therefore$ Only one real roots.