Find all values of x satisfying the given conditions.
-$y _ { 1 } = \frac { x } { x - 7 } + 8 , y _ { 2 } = 6 \sqrt { \frac { x } { x - 7 } }$, and $y _ { 1 } = y _ { 2 }$
A) $\frac { 112 } { 15 } , \frac { 28 } { 3 }$
B) 4,2
C) $\frac { 28 } { 3 } , 14$
D) $- \frac { 112 } { 15 } , - \frac { 28 } { 3 }$

Question

Quizplus · Accepted Answer

To find the values of $x$ that satisfy $y_1 = y_2$, we set the expressions for $y_1$ and $y_2$ equal to each other and solve for $x$:$$\frac{x}{x-7} + 8 = 6\sqrt{\frac{x}{x-7}}$$Squaring both sides to eliminate the square root gives:$$\left(\frac{x}{x-7} + 8\right)^2 = 36\frac{x}{x-7}$$Expanding and simplifying this equation will eventually lead to a quadratic equation in terms of $x$. Solving this quadratic equation will give the values of $x$ that satisfy the original condition. The correct values, after solving the quadratic equation, are $\frac{112}{15}$ and $\frac{28}{3}$, which corresponds to choice A.

Find All Values of X Satisfying the Given Conditions y1=xx−7+8,y2=6xx−7y _ { 1 } = \frac { x } { x - 7 } + 8 , y _ { 2 } = 6 \sqrt { \frac { x } { x - 7 } }y1​=x−7x​+8,y2​=6x−7x​​

Find All Values of X Satisfying the Given Conditions $y _ { 1 } = \frac { x } { x - 7 } + 8 , y _ { 2 } = 6 \sqrt { \frac { x } { x - 7 } }$