Solve the equation.
-$$9 + 24 u ^ { - 2 } = 58 u ^ { - 1 }$$

Question

Quizplus · Accepted Answer

To solve the equation $9 + 24u^{-2} = 58u^{-1}$, we first rewrite it in a more familiar form by using the substitution $v = u^{-1}$, which gives us $9 + 24v^2 = 58v$. Rearranging this equation, we get $24v^2 - 58v + 9 = 0$. Solving this quadratic equation using the quadratic formula, where $a = 24$, $b = -58$, and $c = 9$, we find the roots of $v$. Substituting back $u^{-1} = v$, we solve for $u$ to find the solutions. The correct solutions are $u = \frac{4}{9}$ and $u = 6$, which corresponds to choice B.

Solve the Equation 9+24u−2=58u−19 + 24 u ^ { - 2 } = 58 u ^ { - 1 }9+24u−2=58u−1

Solve the Equation $9 + 24 u ^ { - 2 } = 58 u ^ { - 1 }$