Solve Equations That Are Quadratic in Form
Solve the equation by making an appropriate substitution.
-$$x ^ { 1 / 2 } - 19 x ^ { 1 / 4 } + 90 = 0$$
A) $\{ 10,000,6561 \}$
B) $\{ 100,81 \}$
C) $\{ - 10 , - 9 \}$
D) $\{ 10,9 \}$

Question

Quizplus · Accepted Answer

Let $u = x ^ { 1 / 4 } $. Then $u^4 = x$. Substituting, we get$$u^4 - 19 u^2 + 90 = 0$$$$(u^2 - 9)(u^2 - 10) = 0$$$$u^2 = 9, 10$$$$u = \pm 3, \pm \sqrt { 10 }$$$$x ^ { 1 / 4 } = \pm 3, \pm \sqrt { 10 }$$$$x = 81, 100, 10, 9$$

Solve Equations That Are Quadratic in Form Solve the Equation x1/2−19x1/4+90=0x ^ { 1 / 2 } - 19 x ^ { 1 / 4 } + 90 = 0x1/2−19x1/4+90=0

Solve Equations That Are Quadratic in Form
Solve the Equation $x ^ { 1 / 2 } - 19 x ^ { 1 / 4 } + 90 = 0$