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Surds

solve: X2 +...

Question

solve: $(X^{2} + 3 X) (2 X + 3) - 16 \frac{2 X + 3}{X^{2} + 3 X} \geq 0$

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Solution

$(X^{2} + 3 X) (2 X + 3) - 16 \frac{(2 X + 3)}{(X^{2} + 3 X)} \geq 0$

$(X^{2} + 3 X) (2 X + 3) \geq 16 \frac{(2 X + 3)}{(X^{2} + 3 X)}$

$(X^{2} + 3 X) \geq 16 \frac{1}{(X^{2} + 3 X)}$

$(X^{2} + 3 X)^{2} \geq 16$

$(X^{2} + 3 X) \geq \sqrt{16}, (X^{2} + 3 X) \leq \sqrt{16}$

$(X^{2} + 3 X) \geq 4, (X^{2} + 3 X) \leq 4$

$X \geq 1, X \leq - 4$

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