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Formula for Sum of n Terms of an AP

Solve |x2+x...

Question

Solve $| x^{2} + x - 4 | = | x^{2} - 4 | + | x |$ .

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Solution

$∣ ∣ x^{2} + x - 4 ∣ ∣ = ∣ ∣ x^{2} - 4 ∣ ∣ + | x |$

$x^{2} + x - 4 \geq 0 : x \leq \frac{- \sqrt{17} - 1}{2} o r x \geq \frac{\sqrt{17} - 1}{2}$

$x^{2} + x - 4 < 0 : \frac{- \sqrt{17} - 1}{2} < x < \frac{\sqrt{17} - 1}{2}$

$x^{2} - 4 \geq 0 : x \leq - 2 o r x \geq 2, ∣ ∣ x^{2} - 4 ∣ ∣ = x^{2} - 4$

$x^{2} - 4 < 0 : - 2 < x < 2, ∣ ∣ x^{2} - 4 ∣ ∣ = - (x^{2} - 4)$

$x \geq 0 : x \geq 0, | x | = x$

$x < 0 : x < 0, | x | = - x$

$∴ - 2 \leq x \leq 0 o r x \geq 2$

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