Find a number such that the sum of the number and its reciprocal is $\frac { 65 } { 8 }$ .
A) 8 or $\frac { 1 } { 8 }$
B) 11 or 1
11
C) 12 or $\frac { 1 } { 12 }$
D) $9$ or $\frac { 1 } { 9 }$
E) $10$ or $\frac { 1 } { 10 }$

Question

Quizplus · Accepted Answer

Let the number be $x$. According to the given condition, $x + \frac{1}{x} = \frac{65}{8}$. Multiplying both sides by $x$, we get $x^2 + 1 = \frac{65}{8}x$. Rearranging, we get $x^2 - \frac{65}{8}x + 1 = 0$. This is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 1$, $b = -\frac{65}{8}$, and $c = 1$. Solving this equation, we find that the solutions are $x = 8$ and $x = \frac{1}{8}$, which corresponds to option A.

Find a Number Such That the Sum of the Number 658\frac { 65 } { 8 }865​

Find a Number Such That the Sum of the Number $\frac { 65 } { 8 }$