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October 2nd, 2016, 12:35 PM   #1
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Hard Fraction problem

I'm having quite a bit of trouble with this question.

If x + y = 4 and xy = 5, then 1/x + 1/y = ?

(Note: 1/x and 1/y are written were written in fraction form)
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October 2nd, 2016, 01:08 PM   #2
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There are no real solutions. I'll try and figure out what the complex ones are.

EDIT: This is false. It ends up with one real solution. I underestimated this problem.

EDIT: No, wait, I overestimated it.

Last edited by edrudathec; October 2nd, 2016 at 01:23 PM.
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October 2nd, 2016, 01:12 PM   #3
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Quote:
Originally Posted by IamHere View Post
I'm having quite a bit of trouble with this question.

If x + y = 4 and xy = 5, then 1/x + 1/y = ?

(Note: 1/x and 1/y are written were written in fraction form)
Are you sure you've got those two equations right?

Are you supposed to know about complex numbers yet?
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October 2nd, 2016, 01:13 PM   #4
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Quote:
Originally Posted by edrudathec View Post
There are no real solutions.
This is incorrect. Complex numbers are not required for this problem, only fractions.

Have you tried doing the sum $\frac1x + \frac1y$?
Thanks from edrudathec

Last edited by v8archie; October 2nd, 2016 at 01:17 PM.
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October 2nd, 2016, 01:25 PM   #5
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Try thinking of it like

x + y = 4
xy = 5
xy - 1 = 4

x + y = xy - 1

And then divide and substitute xy to solve from there.
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October 2nd, 2016, 01:30 PM   #6
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Trying to solve for x and y (which is what I did) is not a good way to solve this, because they're both complex numbers.
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October 2nd, 2016, 01:31 PM   #7
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Given that it is described as a fractions problem, I am 95% certain that the OP is supposed to evaluate the sum he was given.
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October 2nd, 2016, 01:44 PM   #8
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I didn't mean solve it that way: solve for x=? and y=?

Like if you divided and substituted xy then:

x + y = xy - 1 (Divide by xy)

1/y + 1/x = 1 - 1/xy (xy = 5)

1/x + 1/y = 1 - 1/5

Answer: 4/5. No complex numbers involved.
I laid out the steps divide and substitute xy so that if u tried them you would see that the sum could easily be solved for.

Last edited by GeoLifeScienceGuy; October 2nd, 2016 at 01:47 PM.
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October 2nd, 2016, 02:15 PM   #9
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Quote:
Originally Posted by GeoLifeScienceGuy View Post
I didn't mean solve it that way: solve for x=? and y=?

Like if you divided and substituted xy then:

x + y = xy - 1 (Divide by xy)

1/y + 1/x = 1 - 1/xy (xy = 5)

1/x + 1/y = 1 - 1/5

Answer: 4/5. No complex numbers involved.
I laid out the steps divide and substitute xy so that if u tried them you would see that the sum could easily be solved for.
I didn't mean that you did mean solve it that way.

I wasn't sure what you meant by divide and substitute xy at first, so I advocated for v8archie's solution, which I think is the best out of the three.

Sorry for the confusion.
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October 2nd, 2016, 02:16 PM   #10
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It is even easier, and better practice for the OP to simply do the given sum.
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