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Reducing Equations to Simpler Form

Solve |x2 +...

Question

Solve $| x^{2} + 4 x + 3 | + 2 x + 5 = 0$

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Solution

Case $I$
$x^{2} + 4 x + 3 + 2 x + 5 = 0$
$⟹ x^{2} + 6 x + 8 = 0$
$⟹ x^{2} + 4 x + 2 x + 8 = 0$
$⟹ x (x + 4) + 2 (x + 4) = 0$
$⟹ x = - 2, - 4$
Case $I I$
$- x^{2} - 4 x - 3 + 2 x + 5 = 0$
$⟹ - x^{2} - 2 x - 2 = 0$
$⟹ x^{2} + 2 x + 2 = 0$
$⟹ x = \frac{- 2 \pm \sqrt{4 - 8}}{2}$
$⟹ x = - 1 \pm i$

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Reducing Equations to Simpler Form

Standard VIII Mathematics

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