Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The complete set of values of x satisfying the equation x 2 . 2 x+1 + 2 |x–3| + 2 = x 2 .2 |x–3|+ 4 + 2 x–1 is
A
[3, ∞ )
B
∪ (3, ∞ )
C
D
∪ [3, ∞ )
Text Solution
Verified by ExpertsThe correct answer is:
D
Case -I : x ≥ 3
x 2 .2 x+1 + 2 x–3+2 = x 2 2 x–3+4 + 2 x–1
⇒ 0 = 0 ⇒ x ∈ [3, ∞ )
Case- II : x ∈ [– ∞ ,3)
x 2 2 x+1 + 2 3–x+2 = x 2 2 3–x+4 + 2 x–1
⇒ 2x 2 2 x + 32.2 –x = 128x 2 2 –x + 
⇒ 
⇒ (4x 2 –1) [2 x – 64.2 –x ) = 0
⇒ x = ± 
, x = 3
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