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Solve |x 2 + 4x + 3 | + 2x + 5 = 0

Solve |x2 + 4x + 3 | + 2x + 5 = 0

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
sol. The Given equation is,
|x2 + 4x + 3 | + 2x + 5 = 0
Now there can be two cases.
Case I : x2 + 4x + 3 ≥ 0 ⇒ (x + 1) (x + 3) ≥ 0
⇒ x ∈ (- ∞, -3] ∪ [ -1, ∞) . . . . . . . . . . . . . . . (i)
Then given equation becomes,
⇒ x2 + 6x + 8 = 0
⇒ (x + 4) (x + 2) = 0 ⇒ x = -4, -2
But x = -2 does not satisfy (i), hence rejected
∴ x = -4 is the sol.
Case II : x2 + 4x + 3 < 0
⇒ (x + 1) (x + 3) < 0
⇒ x ∈ (-3, -1) . . . . . . . . . . . . . . . . . . . . (ii)
Then given equation becomes,
-(x2 + 4x + 3) + 2x + 5 = 0
⇒ -x2 – 2x + 2 = 0 ⇒ x2 + 2x – 2 = 0
⇒ x = -2 ±√4 + 8/2
⇒ x = -1 + √3, -1 - √3
Out of which x = -1 - √3 is sol.
Combining the two cases we get the solutions of given equation as x = -4, -1 - √3.

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