Solve the equation.
-$$x ^ { 6 } + 9 = 9 x ^ { 4 } + x ^ { 2 }$$
A) $\{ - 3,3 , - i , i \}$
B) $\{ - 3,3 , - 1,1 \}$
C) $\{ - 3,3 , - 1,1 , - 3 i , 3 i \}$
D) $\{ - 3,3 , - 1,1 , - i , i \}$

Question

Quizplus · Accepted Answer

Rearranging the equation gives $x^6 - 9x^4 - x^2 + 9 = 0$. Factoring by grouping or using substitution (e.g., let $y = x^2$, then solve $y^3 - 9y^2 - y + 9 = 0$) can lead to the realization that the equation can be factored to include terms that correspond to the solutions given in option D: $\{-3, 3, -1, 1, -i, i\}$. These solutions include real numbers $-3, 3, -1, 1$ and complex numbers $-i, i$, which satisfy the original equation when substituted back.

Solve the Equation x6+9=9x4+x2x ^ { 6 } + 9 = 9 x ^ { 4 } + x ^ { 2 }x6+9=9x4+x2

Solve the Equation $x ^ { 6 } + 9 = 9 x ^ { 4 } + x ^ { 2 }$