QJEEM20Maf7f9: JEE Main 2020 Mathematics - Class 11 JEEM20Maf7f9 Solution: Let S be the set of all real roots of the equation, 3 x (3 x –…

Let 3^x = t ; t > 0

t(t – 1) + 2 = |t – 1| + |t – 2|

t² – t + 2 = |t – 1| + |t – 2|

Case-I : t < 1

t² – t + 2 = 1 – t + 2 – t

$\Rightarrow$ t² + 2 = 3 – t

$\Rightarrow$ t² + t – 1 = 0

$\Rightarrow$ t = ${{ - 1 \pm \sqrt 5 } \over 2}$

$\Rightarrow$ t = ${{\sqrt 5 - 1} \over 2}$ [ As t > 0]

Case-II : 1 $\le$ t < 2

$\Rightarrow$ t² – t + 2 = t – 1 + 2 – t

$\Rightarrow$ t² – t + 1 = 0

D < 0 so no real solution.

Case-III : t $\ge$ 2

$\Rightarrow$ t² – t + 2 = t – 1 + t – 2

$\Rightarrow$ t² – 3t - 5 = 0

$\Rightarrow$ D < 0 so no real solution.