Question

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

Answer 1

\[x + \frac{ 1 }{ x } = \frac{ 65 }{8 }\]

multiply by x and its the same idea

Answer 2

how do i multiply x by 65/8

Answer 3

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

Answer 4

so is it 8,1/8

Answer 5

\(x + \dfrac{1}{x} = \dfrac{65}{8} \)

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.

Answer 6

thanks mathstudent your the man

Answer 7

You're welcome.