For the given rational function, find all values of x for which y has the indicated value.
-$$y = 8 x + \frac { 15 } { x } ; \quad y = 26$$
A) $\frac { 3 } { 4 } , \frac { 5 } { 2 }$
B) $\frac { 2 } { 3 } , \frac { 4 } { 5 }$
C) $\frac { 3 } { 2 } , \frac { 5 } { 4 }$
D) $\frac { 4 } { 3 } , \frac { 2 } { 5 }$

Question

Quizplus · Accepted Answer

To find the values of $x$ for which $y = 26$, substitute $y$ with $26$ in the given equation and solve for $x$:$$26 = 8x + \frac{15}{x}$$Multiplying both sides by $x$ to clear the fraction gives:$$26x = 8x^2 + 15$$Rearrange the equation to set it to 0:$$8x^2 - 26x + 15 = 0$$Factoring or using the quadratic formula, we find the roots $x = \frac{3}{4}$ and $x = \frac{5}{2}$, which correspond to choice A.

For the Given Rational Function, Find All Values of X y=8x+15x;y=26y = 8 x + \frac { 15 } { x } ; \quad y = 26y=8x+x15​;y=26

For the Given Rational Function, Find All Values of X $y = 8 x + \frac { 15 } { x } ; \quad y = 26$