Solve Difficult Equation: x = 4

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SUMMARY

The equation x = 4 was discussed in terms of its solvability, with participants concluding that while a graphical solution is straightforward, an algebraic solution is not feasible. The conversation highlighted the limitations of algebraic methods for certain equations, emphasizing the utility of numerical methods such as Newton's method for finding solutions. Participants noted that if a rational solution exists, it is likely to be integral, specifically pointing out that x = 4 is a valid solution.

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  • Basic concepts of rational and integral numbers
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hey all,

a friend gave me this equation and required that i solve it:

http://www.geocities.com/mazen_zone/Untitled.jpg

I could only solve it graphically and the answer was (x = 4),
so i wonder if there is an algebraic solution for it ?
 
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I don't think there is any way to solve it algebraically.

With such equations, it's easy to create them, while terribly annoying to solve without calculators to solve it numerically for you. I think your friend may have caused you a headache for laughs :wink:
 
Last edited:
Mentallic said:
I don't think there is any way to solve it algebraically.

With such equations, it's easy to create them, while terribly annoying to solve without calculators to solve it numerically for you. I think your friend may have caused you a headache for laughs :wink:

lol yeah i guess...thanks anyway.
 
log it, make sqrt(x) the subject, square both sides, and I think that would give you a quadratic which is easy to solve.

edit: Sorry I just realized that's a dumb idea. Yeah, I don't think there's any way to solve it analytically.
 
Anyway, not with log and all. Since you have a sum of the two, the log would not apply in that sense.

Cheers
 
Calculators use Newton's method to solve equations (including this type of equations of course)
maybe that's the only analytic way to solve it, but i don't know how to use this method :smile:
 
"Algebraically" is a vague term. It is easy to see that if there is a rational answer then it must actually be integral, and in fact x is a square. This leads you to try 1,4 and get the answer (almost) immediately.

If there isn't such a nice easy to spot idea, then the solution is almost certainly going to be nasty, transcendental and impossible to write down in any nice way, so don't bother to try.
 

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