Solve the equation after making an appropriate substitution.
-$$x ^ { 1 / 2 } - 9 x ^ { 1 / 4 } + 18 = 0$$
A) $\{ 81,1296 \}$
B) $\{ 9,36 \}$
C) $\{ - 3 , - 6 \}$
D) $\{ 3,6 \}$

Question

Quizplus · Accepted Answer

Let $u = x ^ { 1 / 4 } $. Then $u^4 = x$. Substituting into the given equation gives$$u^2 - 9u + 18 = 0$$$$(u - 6)(u - 3) = 0$$$$u = 6, 3$$$$x ^ { 1 / 4 } = 6, 3$$$$x = 1296, 81$$

Solve the Equation After Making an Appropriate Substitution x1/2−9x1/4+18=0x ^ { 1 / 2 } - 9 x ^ { 1 / 4 } + 18 = 0x1/2−9x1/4+18=0

Solve the Equation After Making an Appropriate Substitution $x ^ { 1 / 2 } - 9 x ^ { 1 / 4 } + 18 = 0$