JEE Main 2021 — Sets And Relations Question with Solution
From: JEE Main 2021 (Online) 16th March Morning Shift
Question
The number of elements in the set {x R : (|x| 3) |x + 4| = 6} is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B2
Step-by-step explanation
Case 1 :
x 4
(x 3)(x 4) = 6
(x + 3)(x + 4) = 6
x2 + 7x + 6 = 0
x = 1 or 6
but x 4
x = 6
Case 2 :
x (4, 0)
(x 3)(x + 4) = 6
x2 7x 12 6 = 0
x2 + 7x + 18 = 0
D < 0 No solution
Case 3 :
x 0
(x 3)(x + 4) = 6
x2 + x 12 6 = 0
x2 + x 18 = 0
x =
x = only
x 4
(x 3)(x 4) = 6
(x + 3)(x + 4) = 6
x2 + 7x + 6 = 0
x = 1 or 6
but x 4
x = 6
Case 2 :
x (4, 0)
(x 3)(x + 4) = 6
x2 7x 12 6 = 0
x2 + 7x + 18 = 0
D < 0 No solution
Case 3 :
x 0
(x 3)(x + 4) = 6
x2 + x 12 6 = 0
x2 + x 18 = 0
x =
x = only
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