What is the solution of the inequality 9 - x^2<0?

Mathematics

1 answer:

Dmitry_Shevchenko [17]2 years ago

5 0

Answer:

$x < -3\quad \mathrm{or}\quad \:x > 3$

Step-by-step explanation:

Given:

$9-x^2 < \:0$

Solve:

$\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}$

$9-x^2-9 < 0-9$

$\mathrm{Simplify}$

$-x^2 < -9$

$Multiply\:both\:sides\:by\:-1\:$

$\left(-x^2\right)\left(-1\right) > \left(-9\right)\left(-1\right)$

$\mathrm{Simplify}$

$x^2 > 9$

$\mathrm{For\:}u^n\: > \:a\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\: < \:-\sqrt[n]{a}\:or\:u\: > \:\sqrt[n]{a}$

$x < -\sqrt{9}\quad \mathrm{or}\quad \:x > \sqrt{9}$

$\sqrt{9}=3$

$x < -3\quad \mathrm{or}\quad \:x > 3$

~lenvy~

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