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Little integer problem

  • #1
ok,

a/b c/d

a,b,c,d are all integers
b and d are > 0

find a number inbetween a/b and b/d using a,b,c,d that is an irrational number.

thanks :!!)
 

Answers and Replies

  • #2
CarlB
Science Advisor
Homework Helper
1,214
12
The difference between the two rational numbers is

[tex]\frac{ad-bc}{bd}[/tex]

If you can find an irrational number that is smaller than this, you can add it to the lesser of {a/d, b/c}.

Carl
 
  • #3
StatusX
Homework Helper
2,564
1
You could pick a strictly increasing curve (like y=x^2, for x>0), find the x values that generate these two fractions as y values, and find the y value for the number halfway (or anywhere) between these two x values. It's a safe bet this will be an irrational number.
 
  • #4
CarlB said:
The difference between the two rational numbers is

[tex]\frac{ad-bc}{bd}[/tex]

If you can find an irrational number that is smaller than this, you can add it to the lesser of {a/d, b/c}.

Carl
so that will work for sure carl?
 

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