Find all values of x satisfying the given conditions.
-$y _ { 1 } = \frac { x } { x - 3 } + 8 , y _ { 2 } = 6 \sqrt { \frac { x } { x - 3 } }$, and $y _ { 1 } = y _ { 2 }$
A) $\frac { 16 } { 5 } , 4$
B) 4,6
C) 4,2
D) $- \frac { 16 } { 5 } , - 4$

Question

Quizplus · Accepted Answer

To find the values of $x$ that satisfy $y_1 = y_2$, we set $\frac{x}{x-3} + 8 = 6\sqrt{\frac{x}{x-3}}$. This equation can be solved by squaring both sides and simplifying, or by recognizing that both sides represent transformations of the same basic function of $x$, leading to the solutions $x = \frac{16}{5}$ and $x = 4$.

Find All Values of X Satisfying the Given Conditions y1=xx−3+8,y2=6xx−3y _ { 1 } = \frac { x } { x - 3 } + 8 , y _ { 2 } = 6 \sqrt { \frac { x } { x - 3 } }y1​=x−3x​+8,y2​=6x−3x​​

Find All Values of X Satisfying the Given Conditions $y _ { 1 } = \frac { x } { x - 3 } + 8 , y _ { 2 } = 6 \sqrt { \frac { x } { x - 3 } }$