Solve - 12x-4x2-9 - 1-

| 12x / 4 x ^ 2 +9 nbsp;| ≤ 1⇒ 1≤ 12x / 4 x ^ 2 +9 ≤ 1 since 4 x ^ 2 +9 is +ve for all real x We can multiply the inequality by ...

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(a + b)^2 Expansion and Visualisation

Solve | 12x...

Question

Solve $∣ ∣ ∣ \frac{12 x}{4 x^{2} + 9} ∣ ∣ ∣ \leq 1.$

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Solution

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\frac{(4 x + 1)^{2} + (2 x + 3)^{2}}{4 x^{2} + 12 x + 9} = \frac{61}{36}

\frac{(4 x + 1)^{2} + (2 x + 3)^{2}}{4 x^{2} + 12 x + 9} = \frac{61}{36}

x

\begin{matrix} (5 x - 1) < & {(x + 1)}^{2} < & (7 x - 3) I & I I & I I I \end{matrix}

S o l v e ∣ ∣ ∣ \frac{12 x}{4 x^{2} + 9} ∣ ∣ ∣ \leq 1

{log}_{(2 x + 3)} ({6 x}^{2} + 23 x + 21) = 4 - {log}_{(3 x + 7)} ({4 x}^{2} + 12 x + 9)

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7 - 12 x - 4 x^{2}

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