Solve the equation.
-$\sqrt [ 4 ] { \mathrm { x } ^ { 2 } - 13 } = 1$
A) $\{ - \sqrt { 14 } , \sqrt { 14 } \}$
B) $\{ \sqrt { 13 } \}$
C) $\{ \sqrt { 14 } \}$
D) $\{ - \sqrt { 13 } , \sqrt { 13 } \}$

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt[4]{x^2 - 13} = 1$, we first raise both sides to the power of 4 to get rid of the fourth root, resulting in $x^2 - 13 = 1^4$, which simplifies to $x^2 - 13 = 1$. Solving for $x^2$, we get $x^2 = 14$, which means $x = \pm \sqrt{14}$, hence the solutions are $\{-\sqrt{14}, \sqrt{14}\}$.

Solve the Equation x2−134=1\sqrt [ 4 ] { \mathrm { x } ^ { 2 } - 13 } = 14x2−13​=1

Solve the Equation $\sqrt [ 4 ] { \mathrm { x } ^ { 2 } - 13 } = 1$