Question

Solve | x² + 4x + 3| + 2x +5 = 0​

Answer 1

Answer:

x = -4 & (-1-√3) are only the solutions.

Step-by-step explanation:

Given:

| x² + 4x + 3 | + 2x +5 = 0

Case 1 :

${x}^{2} + 4x + 3 > 0$

=> ( x< -3 or x> -1)

${x}^{2} + 4x + 3 + 2x + 5 = 0 \\ \\ {x}^{2} + 6x + 8 = 0 \\ \\ {x}^{2} + 2x + 4x + 8 = 0 \\ \\ x(x + 2) + 4(x + 2) = 0 \\ \\ (x + 4)(x + 2) = 0$

Not equate the factors to zero

we get x = -4 , -2

Now A/c to condition x < -3 or x > -1

So, -2 will be rejected

x = -4 is only the solution ____(i)

CASE 2:

${x}^{2} + 4x + 3 < 0$

( -3 < x < -1)

$- {x}^{2} - 4x - 3 + 2x + 5 = 0 \\ \\ {x}^{2} + 2x - 2 = 0$

Now, -2 can be written as -3 + 1

${x}^{2} + 2x - 3 + 1 = 0 \\ \\ {x}^{2} + 2x + 1 = 3 \\ \\ {(x + 1)}^{2} = 3 \\ \\ |x + 1| = \sqrt{3}$

Now

x = -1 - √3 , -1 + √3

Now A/c to condition x € (-3,-1)

So, -1 + √3 will be rejected

x = -1 - √3 is only the solution ____(ii)

From Eqn (i) & (ii)

we get x = -4 & (-1-√3) are only the solutions.