Find all values of x satisfying the given conditions.
- $$y _ { 1 } = \frac { 1 } { x + 15 } , y _ { 2 } = \frac { 1 } { x } , \text { and } y _ { 1 } + y _ { 2 } = \frac { 1 } { 5 }$$
A) $\frac { - 5 \pm 5 \sqrt { 13 } } { 2 }$
B) $\frac { 25 \pm 5 \sqrt { 13 } } { 2 }$
C) $\frac { - 25 \pm 5 \sqrt { 13 } } { 2 }$
D) $\frac { 5 \pm 5 \sqrt { 13 } } { 2 }$

Question

Quizplus · Accepted Answer

To solve for $x$, combine the given equations: $$\frac { 1 } { x + 15 } + \frac { 1 } { x } = \frac { 1 } { 5 }$$Solving this equation involves finding a common denominator and simplifying, leading to a quadratic equation in $x$. The correct roots of this equation are $\frac { - 5 \pm 5 \sqrt { 13 } } { 2 }$.

Find All Values of X Satisfying the Given Conditions y1=1x+15,y2=1x, and y1+y2=15y _ { 1 } = \frac { 1 } { x + 15 } , y _ { 2 } = \frac { 1 } { x } , \text { and } y _ { 1 } + y _ { 2 } = \frac { 1 } { 5 }y1​=x+151​,y2​=x1​, and y1​+y2​=51​

Find All Values of X Satisfying the Given Conditions $y _ { 1 } = \frac { 1 } { x + 15 } , y _ { 2 } = \frac { 1 } { x } , \text { and } y _ { 1 } + y _ { 2 } = \frac { 1 } { 5 }$