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Question

Mathematics Question on General and Particular Solutions of a Differential Equation

Solution of ∣x2−10∣≤6|x^2 - 10| \le 6 is

A

(2, 4)(2,\,4)

B

(−4, −2)(- 4, \,- 2)

C

(−4, −2)∪(2, 4)(- 4, \,- 2)\cup (2,\, 4)

D

[−4, −2]∪[2, 4][- 4, \,- 2] \cup [2,\, 4]

Answer

[−4, −2]∪[2, 4][- 4, \,- 2] \cup [2,\, 4]

Explanation

Solution

∣x2−10∣≤6 |x^{2}-10 | \le 6 ⇔−6≤x2−10≤6⇔4<x2≤16\Leftrightarrow\quad- 6 \le x^{ 2}-10 \le 6 \Leftrightarrow 4 < x^{2}\le 16 ⇔2≤∣x∣≤4\Leftrightarrow \quad 2 \le |x| \le 4 ∴\therefore\quad either 2≤x≤42 \le x \le 4 or −4≤x≤−2- 4 \le x \le - 2 ∴x∈[−4, −2]∪[2, 4]\therefore\quad x\in \left[- 4, \,- 2\right] \cup \left[2,\,4\right]