Solve Difficult Equation: x = 4

[mazen_zone]

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 ?

 

[Mentallic]

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

 

[mazen_zone]

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

lol yeah i guess...thanks anyway.

 

[logarithmic]

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.

 

[fatra2]

Anyway, not with log and all. Since you have a sum of the two, the log would not apply in that sense.

Cheers

 

[mazen_zone]

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

 

[matt grime]

"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.