The sum of an integer and its reciprocal is 65/8. Find the integer

Question

anonymous · Answer

$$x + \frac{ 1 }{ x } = \frac{ 65 }{8 }$$

multiply by x and its the same idea

anonymous · Answer

how do i multiply x by 65/8

mathstudent55 · Answer

Multiply both sides by 8x to get rid of the fractions.

anonymous · Answer

so is it 8,1/8

mathstudent55 · Answer

$x + \dfrac{1}{x} = \dfrac{65}{8} $

Multiply both sides by 8x:

$(8x)(x + \dfrac{1}{x}) = (8x)(\dfrac{65}{8}) $

$(8x)(x) + (8x)(\dfrac{1}{x}) = (8x)(\dfrac{65}{8}) $

$(8x)(x) + (8\cancel{x})(\dfrac{1}{\cancel{x}}) = (\cancel{8}x)(\dfrac{65}{\cancel{8}}) $

$8x^2 + 8 = 65x $

$8x^2 - 65x + 8 = 0 $

Now either try factoring or use the quadratic formula.

The answer is 8 or 1/8. You are correct.

anonymous · Answer

thanks mathstudent your the man

mathstudent55 · Answer

You're welcome.