Solve.
-$$x ^ { - 2 } + x ^ { - 1 } = 72$$
A) $\left\{ - \frac { 1 } { 9 } , \frac { 1 } { 8 } \right\}$
B) $\{ 9 , - 8 \}$
C) $\left\{ \frac { 1 } { 9 } , - \frac { 1 } { 8 } \right\}$
D) $\{ - 9,8 \}$

Question

Quizplus · Accepted Answer

To solve the equation $x^{-2} + x^{-1} = 72$, let $y = x^{-1}$, then the equation becomes $y^2 + y - 72 = 0$. Factoring gives $(y + 9)(y - 8) = 0$, so $y = -9$ or $y = 8$. Since $y = x^{-1}$, we have $x = -\frac{1}{9}$ or $x = \frac{1}{8}$, which matches choice A.

Solve - x−2+x−1=72x ^ { - 2 } + x ^ { - 1 } = 72x−2+x−1=72

Solve
- $x ^ { - 2 } + x ^ { - 1 } = 72$