Solve for real roots.
-$x ^ { 2 / 5 } - x ^ { 1 / 5 } - 6 = 0$
A) $x = 243 , - 32$
B) $x = 3 , - 2$
C) $x = - 3,2$
D) $x = - 243,32$

Name: Solve for real roots. -$x ^ { 2 / 5 } - x ^ { 1 / 5 } - 6 = 0$ A) $x = 243 , - 32$ B) $x = 3 , - 2$ C) $x = - 3,2$ D) $x = - 243,32$
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Question

Quizplus · Accepted Answer

Let $y = x^{1/5}$, then the equation becomes $y^2 - y - 6 = 0$, which factors to $(y-3)(y+2) = 0$. Solving for $y$ gives $y = 3$ or $y = -2$. Substituting back for $x$, $x = 3^5 = 243$ and $x = (-2)^5 = -32$.

Solve for Real Roots x2/5−x1/5−6=0x ^ { 2 / 5 } - x ^ { 1 / 5 } - 6 = 0x2/5−x1/5−6=0

Solve for Real Roots $x ^ { 2 / 5 } - x ^ { 1 / 5 } - 6 = 0$