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`        Solve |x2 + 4x + 3 | + 2x + 5 = 0`
5 years ago Navjyot Kalra
654 Points
```
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.

```
5 years ago
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