QJEEM21Mab518: JEE Main 2021 Mathematics - Class 11 JEEM21Mab518 Solution: The number of elements in the set {x R : (

Case 1 :

x $\le$ $-$ 4

( $-$ x $-$ 3)( $-$ x $-$ 4) = 6

$\Rightarrow$ (x + 3)(x + 4) = 6

$\Rightarrow$ x² + 7x + 6 = 0

$\Rightarrow$ x = $-$ 1 or $-$ 6

but x $\le$ $-$ 4

x = $-$ 6

Case 2 :

x $\in$ ( $-$ 4, 0)

( $-$ x $-$ 3)(x + 4) = 6

$\Rightarrow$ $-$ x² $-$ 7x $-$ 12 $-$ 6 = 0

$\Rightarrow$ x² + 7x + 18 = 0

D < 0 No solution

Case 3 :

x $\ge$ 0

(x $-$ 3)(x + 4) = 6

$\Rightarrow$ x² + x $-$ 12 $-$ 6 = 0

$\Rightarrow$ x² + x $-$ 18 = 0

x = ${{ - 1 \pm \sqrt {1 + 72} } \over 2}$

$\therefore$ x = ${{\sqrt {73} - 1} \over 2}$ only