Thread: Equation

Can Anyone solve this equation?

Originally Posted by clearwar

Can Anyone solve this equation?

yes

this is actually very simple algebra, and the answer is "2'. the working is a little troublesome to write as a reply post, as it is kind of long, and i might make mistakes as im writing it but it does not require hard thinking, as long as you are good with the basic algebra, you should be fine in solving this question.

So x is algebric...?

Originally Posted by clearwar

So x is algebric...?

X is a variable. The equation is algebraic and any solution will be an algebraic solution.

The equation is actually quartic in the variable y= sqrt(x).

The solition x=2 is obvious by inspection.

It can be reduced from there, although it appears a bit tedious to reduce the order of the polynomial (in y) and find all possible solutions. I have not carried this out.

There is a general formula for the solution of quartic polynomials by radicals. It is tedious.

The equation is algebraic and any solution will be an algebraic solution.

X rappresents the area so i must put in evidence is algebrical and not trascendental...(i build the equation following some geometric tricks supponing to compare a circle and a square having the side )

one solution must be algebrai 3.1415 is it right?

Originally Posted by clearwar

The equation is algebraic and any solution will be an algebraic solution.

X rappresents the area so i must put in evidence is algebrical and not trascendental...(i build the equation following some geometric tricks supponing to compare a circle and a square having the side )

one solution must be algebrai 3.1415 is it right?

Then you made a mistake.

Pi is not algebraic. That is well known.

The related fact that it is impossible to construct a square of area pi using a rule and straightedge is also known.

PM

wait, im not quite following the , in relation with this question.. the question you proposed is just simple algebra, with nothing more than tedious workings.

My trouble is if it is possible matematically define a square of area . If so I can easly compare it to a circle to define a formula that calculates through pitagora. Anywhere the equation in x (where x is pi) is futile?

Originally Posted by clearwar

My trouble is if it is possible matematically define a square of area . If so I can easly compare it to a circle to define a formula that calculates through pitagora. Anywhere the equation in x (where x is pi) is futile?

It is not possible to mathematically construct a square of area pi.

You can define a square to have any area that you want, but if you define a square to have area pi then you cannot construct a square of area 1.

clearwar, you're never going to find a solution until you understand the actual problem you're attempting to solve. And then once you understand that problem, you might can see that it honestly doesn't have a solution.