need help

[flew62999]

The sum of an integer and its reciprocal is 26/5. Find the integer.

I came up with:

x + 1/x = 26/5

is this correct? do I multiply each side by 5 or 5x?
Please help.

Thanks.

 

[rahidz2003]

Yes, you set the correct equation up...

Now, what I'd do is combine x + (1/x) into one fraction...

x+(1/x)=
(x/1)+(1/x)=
((x^2)/x)+(1/x)=
(x^2+1)/x

So, with (x^2+1)/x=26/5,

I'd cross-multiply and solve for x

5*(x^2+1)=26x

5x^2+5-26x=0

5x^2-26x+5=0

Then just use the quadratic formula and find x

 

[soroban]

Hello, flew62999!

The sum of an integer and its reciprocal is 26/5. Find the integer.

I came up with: x + 1/x = 26/5

Is this correct? . . . . yes!

Do I multiply each side by 5 or 5x? . . . . by 5x

. . . . . . . . . . . . . . . .1 . . . .26
We have: . 5x [x + -- . = . --- ]
. . . . . . . . . . . . . . . .x . . . . 5

. . and then: . 5x² + 5 . = . 26x

We have the quadratic: . 5x² - 26x + 5 . = . 0

. . which factors: . (x - 5)(5x - 1) . = . 0

. . and has roots: . x = 5, 1/5

Since x is an integer, the answer is: .x = 5