Make an appropriate substitution and solve the equation.
-$n ^ { 1 / 2 } + 3 n ^ { 1 / 4 } - 40 = 0$
A) $\{ 625 \}$
B) $\{ 625,4,096 \}$
C) $\{ 25 \}$
D) $\{ 5 , - 8 \}$

Question

Quizplus · Accepted Answer

Let $x = n^{1/4}$, then the equation becomes $x^2 + 3x - 40 = 0$. Factoring gives $(x + 8)(x - 5) = 0$, so $x = -8$ or $x = 5$. Since $x = n^{1/4}$, and $n^{1/4}$ must be non-negative, we discard $x = -8$. Thus, $n^{1/4} = 5$, and raising both sides to the fourth power gives $n = 625$.

Make an Appropriate Substitution and Solve the Equation n1/2+3n1/4−40=0n ^ { 1 / 2 } + 3 n ^ { 1 / 4 } - 40 = 0n1/2+3n1/4−40=0

Make an Appropriate Substitution and Solve the Equation $n ^ { 1 / 2 } + 3 n ^ { 1 / 4 } - 40 = 0$