Solve.
-$2 x ^ { 2 / 3 } - 4 x ^ { 1 / 3 } - 30 = 0$
A) $\{ - 27 \rangle$
B) $\{ 125,27 \rangle$
C) $\{ 125 \}$
D) $\{ 125 , - 27 \}$

Question

Quizplus · Accepted Answer

To solve $2 x ^ { 2 / 3 } - 4 x ^ { 1 / 3 } - 30 = 0$, let $y = x^{1/3}$. The equation becomes $2y^2 - 4y - 30 = 0$, which simplifies to $y^2 - 2y - 15 = 0$. Factoring or using the quadratic formula gives $y = 5$ or $y = -3$. Substituting back, $x^{1/3} = 5$ gives $x = 125$, and $x^{1/3} = -3$ gives $x = -27$. Therefore, the solutions are $x = 125$ and $x = -27$.

Solve - 2x2/3−4x1/3−30=02 x ^ { 2 / 3 } - 4 x ^ { 1 / 3 } - 30 = 02x2/3−4x1/3−30=0

Solve
- $2 x ^ { 2 / 3 } - 4 x ^ { 1 / 3 } - 30 = 0$