Solve the equation by making an appropriate substitution.
-$\left( y - \frac { 15 } { y } \right) ^ { 2 } - 12 \left( y - \frac { 15 } { y } \right) - 28 = 0$
A) $\{ - 5 , - 1,3,15 \}$
B) no solution
C) $\{ - 5,3 \}$
D) $\{ - 2,14 \}$

Question

Quizplus · Accepted Answer

Let $x = y - \frac{15}{y}$. The equation becomes $x^2 - 12x - 28 = 0$. Solving this quadratic equation gives $x = -2$ or $x = 14$. Substituting back for $x$, we solve for $y$ in $y - \frac{15}{y} = -2$ and $y - \frac{15}{y} = 14$, yielding the solutions $-5, -1, 3, 15$.

Solve the Equation by Making an Appropriate Substitution (y−15y)2−12(y−15y)−28=0\left( y - \frac { 15 } { y } \right) ^ { 2 } - 12 \left( y - \frac { 15 } { y } \right) - 28 = 0(y−y15​)2−12(y−y15​)−28=0

Solve the Equation by Making an Appropriate Substitution $\left( y - \frac { 15 } { y } \right) ^ { 2 } - 12 \left( y - \frac { 15 } { y } \right) - 28 = 0$