# 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
Mentor
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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.

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