Make an appropriate substitution and solve the equation.
-$\left( m - \frac { 12 } { m } \right) ^ { 2 } - 10 \left( m - \frac { 12 } { m } \right) - 11 = 0$
A) $\{ - 4 , - 1,3,12 \}$
B) $\{ - 1,11 \}$
C) $\{ - 12 , - 4,1,3 \}$
D) $\{ 1 , - 11 \}$

Question

Quizplus · Accepted Answer

Let $x = m - \frac{12}{m}$. The equation becomes $x^2 - 10x - 11 = 0$. Factoring or using the quadratic formula gives $x = -1$ or $x = 11$. Substituting back for $x$, we solve $m - \frac{12}{m} = -1$ and $m - \frac{12}{m} = 11$, leading to the solutions $m = -4, -1, 3, 12$.

Make an Appropriate Substitution and Solve the Equation (m−12m)2−10(m−12m)−11=0\left( m - \frac { 12 } { m } \right) ^ { 2 } - 10 \left( m - \frac { 12 } { m } \right) - 11 = 0(m−m12​)2−10(m−m12​)−11=0

Make an Appropriate Substitution and Solve the Equation $\left( m - \frac { 12 } { m } \right) ^ { 2 } - 10 \left( m - \frac { 12 } { m } \right) - 11 = 0$