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Which equation has both $6$ and $-6$ as possible values of $x$ ? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $x^2 = 3$ $\newline$ (B) $x^3 = 3$ $\newline$ (C) $x^2 = 12$ $\newline$ (D) $x^3 = 12$ $\newline$ (E) $x^2 = 36$ $\newline$ (F) $x^3 = 36$

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Solve complex trigonomentric equations

Full solution

Q. Which equation has both

6

and

-6

as possible values of

x

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

x^2 = 3

\newline

(B)

x^3 = 3

\newline

(C)

x^2 = 12

\newline

(D)

x^3 = 12

\newline

(E)

x^2 = 36

\newline

(F)

x^3 = 36

Check Equation (A): Step $1$ : Check equation (A) $x^2 = 3$ . $\newline$ Calculate $x^2$ when $x = 6$ and $x = -6$ . $\newline$ $6^2 = 36$ and $(-6)^2 = 36$ . $\newline$ Since $36 \neq 3$ , neither $6$ nor $-6$ are solutions for equation (A).
Check Equation (B): Step $2$ : Check equation (B) $x^3 = 3$ . $\newline$ Calculate $x^3$ when $x = 6$ and $x = -6$ . $\newline$ $6^3 = 216$ and $(-6)^3 = -216$ . $\newline$ Since $216 \neq 3$ and $-216 \neq 3$ , neither $6$ nor $-6$ are solutions for equation (B).
Check Equation (C): Step $3$ : Check equation (C) $x^2 = 12$ . $\newline$ Calculate $x^2$ when $x = 6$ and $x = -6$ . $\newline$ $6^2 = 36$ and $(-6)^2 = 36$ . $\newline$ Since $36 \neq 12$ , neither $6$ nor $-6$ are solutions for equation (C).
Check Equation (D): Step $4$ : Check equation (D) $x^3 = 12$ . $\newline$ Calculate $x^3$ when $x = 6$ and $x = -6$ . $\newline$ $6^3 = 216$ and $(-6)^3 = -216$ . $\newline$ Since $216 \neq 12$ and $-216 \neq 12$ , neither $6$ nor $-6$ are solutions for equation (D).
Check Equation (E): Step $5$ : Check equation (E) $x^2 = 36$ . $\newline$ Calculate $x^2$ when $x = 6$ and $x = -6$ . $\newline$ $6^2 = 36$ and $(-6)^2 = 36$ . $\newline$ Since $36 = 36$ , both $6$ and $-6$ are solutions for equation (E).
Check Equation (F): Step $6$ : Check equation (F) $x^3 = 36$ . $\newline$ Calculate $x^3$ when $x = 6$ and $x = -6$ . $\newline$ $6^3 = 216$ and $(-6)^3 = -216$ . $\newline$ Since $216 \neq 36$ and $-216 \neq 36$ , neither $6$ nor $-6$ are solutions for equation (F).

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