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Reducing Equations to Simpler Form

Solve x2 + ...

Question

Solve
$(x^{2} + 3 x + 1) (x^{2} + 3 x - 3) \geq 5$

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Solution

$(x^{2} + 3 x + 1) (x^{2} + 3 x - 3) \geq 5$
$(x^{2} + 3 x)^{2} - 2 (x^{2} + 3 x) - 3 \geq 5$
$(x^{2} + 3 x)^{2} - 2 (x^{2} + 3 x) - 8 \geq 0$
$(x^{2} + 3 x - 4) (x^{2} + 3 x + 2) \geq 0$
$x^{2} + 3 x - 4 \geq 0$ $(∵ x^{2} + 3 x + 2 \geq 0$ always $)$
$(x - 1) (x + 4) \geq 0 ⟹ x \in (- \infty, - 4] \cup [1, \infty)$

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Reducing Equations to Simpler Form

Standard VIII Mathematics

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