Solve Equations That Are Quadratic in Form
Solve the equation by making an appropriate substitution.
-$x ^ { 2 / 5 } - x ^ { 1 / 5 } - 6 = 0$
A) $\{ 243 , - 32 \}$
B) $\{ - 243,32 \}$
C) $\{ 3 , - 2 \}$
D) $\{ - 3,2 \}$

Question

Quizplus · Accepted Answer

Let $u = x ^ { 1 / 5 } $. Then $u^2 = x ^ { 2 / 5 }$. Substituting into the original equation gives$$u^2 - u - 6 = 0$$$$(u - 3)(u + 2) = 0$$$$u = 3, -2$$Substituting back into $u = x ^ { 1 / 5 }$ gives$$x ^ { 1 / 5 } = 3, -2$$$$x = 3^5, (-2)^5$$$$x = 243, -32$$

Solve Equations That Are Quadratic in Form Solve the Equation x2/5−x1/5−6=0x ^ { 2 / 5 } - x ^ { 1 / 5 } - 6 = 0x2/5−x1/5−6=0

Solve Equations That Are Quadratic in Form
Solve the Equation $x ^ { 2 / 5 } - x ^ { 1 / 5 } - 6 = 0$