Solve the equation by making an appropriate substitution.
-$$x ^ { 2 / 5 } - x ^ { 1 / 5 } - 2 = 0$$
A) $\{ 32 , - 1 \}$
B) $\{ - 2,1 \}$
C) $\{ - 32,1 \}$
D) $\{ 2 , - 1 \}$

Question

Quizplus · Accepted Answer

Let $u = x^{1/5}$, then the equation becomes $u^2 - u - 2 = 0$, which factors to $(u - 2)(u + 1) = 0$. Solving for $u$ gives $u = 2$ or $u = -1$. Substituting back, $x^{1/5} = 2$ gives $x = 32$, and $x^{1/5} = -1$ gives $x = -1$.

Solve the Equation by Making an Appropriate Substitution x2/5−x1/5−2=0x ^ { 2 / 5 } - x ^ { 1 / 5 } - 2 = 0x2/5−x1/5−2=0

Solve the Equation by Making an Appropriate Substitution $x ^ { 2 / 5 } - x ^ { 1 / 5 } - 2 = 0$