Solve.
-$$x ^ { - 2 } - x ^ { - 1 } - 90 = 0$$
A) $\{ - 10,9 \}$
B) $\left\{ - \frac { 1 } { 10 } , \frac { 1 } { 9 } \right\}$
C) $\{ 10 , - 9 \}$
D) $\left\{ \frac { 1 } { 10 } , - \frac { 1 } { 9 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation $x^{-2} - x^{-1} - 90 = 0$, let $y = x^{-1}$, then the equation becomes $y^2 - y - 90 = 0$. Factoring or using the quadratic formula gives $y = \frac{1}{10}$ or $y = -\frac{1}{9}$. Since $y = x^{-1}$, the solutions for $x$ are $x = 10$ and $x = -\frac{1}{9}$, which corresponds to choice D.

Solve - x−2−x−1−90=0x ^ { - 2 } - x ^ { - 1 } - 90 = 0x−2−x−1−90=0

Solve
- $x ^ { - 2 } - x ^ { - 1 } - 90 = 0$