# Math Question

by Edwin
Tags: math
 P: 167 How would you solve the following system of simultaneous equations for t and b? sin(pi*t) = 0 sin(pi*(t^2 + 35)/(2*t)) = 0 (t^2 + 35)/(2*t) - t/2 - b/2 = 0 t^2/35 +35/t^2 -t/b - b/t = 0 t*b = 35 inquisitively, Edwin G. Schasteen
 Sci Advisor HW Helper P: 3,149 For starters, you should recognize the first equation tells you t is an integer. Likewise, the second tells you $$\frac {t^2 + 35}{2t}$$ is also an integer.
 P: 167 That is true. But how do you solve for t algebraically? Is it even possible to solve these systems of equations without using a graphing calculator? Is it possible using numerical methods? If so, which methods? Inquisitively, Edwin
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## Math Question

Simple observation and common sense go along ways in this sort of problem. I do not know of any numerical method which will work well. The problem comes when you are restricted to the integers. This is not the natural domain of numerical methods which are planted firmly in the real number line.

As Tide pointed out your first equations restricts you to the integers, the second further restricts you to a small set of integers.

Rewrite your 2nd condition as

$$2n = t + \frac {35} t$$

So the RHS is an even integer, there are only 3 integers which can satisfy this equation. Can you complete the problem?
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,894 If you are referring to t, there are 8 integers that will make the right hand side an integer. If you are referring to n, there are 4 integers that will satisfy it.
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 Quote by HallsofIvy If you are referring to t, there are 8 integers that will make the right hand side an integer. If you are referring to n, there are 4 integers that will satisfy it.
I can see 4 integers, 1,5,7,35...I missed the 35 before, But 8? Are you counting negitives as well?
 P: 167 Thanks for the help guys. Notice that the numbers 5 and 7 are prime factors of 35. What I am actually trying to do find is to find a general method to solve these systems of equations, if possible, for numbers Cp that are composites of two odd prime numbers. sin(pi*t) = 0 sin(pi*(t^2 + Cp)/(2*t)) = 0 (t^2 + Cp)/(2*t) - t/2 - b/2 = 0 t^2/Cp +Cp/t^2 -t/b - b/t = 0 t*b = Cp With the domain restriction on t -> D:{1

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