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r-ruslan [8.4K]
2 years ago
10

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

<u><em>~lenvy~</em></u>

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