Which equation has both $\frac{1}{4}$ and $-\frac{1}{4}$ as possible values of $x$ ? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $x^2 = \frac{1}{2}$ $\newline$ (B) $x^3 = \frac{1}{2}$ $\newline$ (C) $x^2 = \frac{1}{16}$ $\newline$ (D) $x^3 = \frac{1}{16}$ $\newline$ (E) $x^2 = \frac{1}{64}$ $\newline$ (F) $x^3 = \frac{1}{64}$

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Algebra 2

Sin, cos, and tan of special angles

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Q. Which equation has both

\frac{1}{4}

and

-\frac{1}{4}

as possible values of

x

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

x^2 = \frac{1}{2}

\newline

(B)

x^3 = \frac{1}{2}

\newline

(C)

x^2 = \frac{1}{16}

\newline

(D)

x^3 = \frac{1}{16}

\newline

(E)

x^2 = \frac{1}{64}

\newline

(F)

x^3 = \frac{1}{64}

Check $x = \frac{1}{4}$ : Step $1$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation (A) $x^2 = \frac{1}{2}$ . $\newline$ Calculation: $\left(\frac{1}{4}\right)^2 = \frac{1}{16}$ and $\left(-\frac{1}{4}\right)^2 = \frac{1}{16}$ . $\newline$ Does not match $\frac{1}{2}$ .
Check $x = -\frac{1}{4}$ : Step $2$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation (B) $x^3 = \frac{1}{2}$ . $\newline$ Calculation: $(\frac{1}{4})^3 = \frac{1}{64}$ and $(-\frac{1}{4})^3 = -\frac{1}{64}$ . $\newline$ Does not match $\frac{1}{2}$ .
Check $x^2 = \frac{1}{16}$ : Step $3$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation (C) $x^2 = \frac{1}{16}$ . $\newline$ Calculation: $\left(\frac{1}{4}\right)^2 = \frac{1}{16}$ and $\left(-\frac{1}{4}\right)^2 = \frac{1}{16}$ . $\newline$ Matches $\frac{1}{16}$ .
Check $x^3 = \frac{1}{16}$ : Step $4$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation $(D) x^3 = \frac{1}{16}$ . $\newline$ Calculation: $(\frac{1}{4})^3 = \frac{1}{64}$ and $(-\frac{1}{4})^3 = -\frac{1}{64}$ . $\newline$ Does not match $\frac{1}{16}$ .
Check $x^2 = \frac{1}{64}$ : Step $5$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation (E) $x^2 = \frac{1}{64}$ . $\newline$ Calculation: $(\frac{1}{4})^2 = \frac{1}{16}$ and $(-\frac{1}{4})^2 = \frac{1}{16}$ . $\newline$ Does not match $\frac{1}{64}$ .
Check $x^3 = \frac{1}{64}$ : Step $6$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation $(F) x^3 = \frac{1}{64}$ . $\newline$ Calculation: $(\frac{1}{4})^3 = \frac{1}{64}$ and $(-\frac{1}{4})^3 = -\frac{1}{64}$ . $\newline$ Matches $\frac{1}{64}$ .