Any idea of solving diophantine equations of degree 3 ?
Please give examples and graphs also ......
Don't spam plzz......
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Answers
Diophantine equations ???
I did those in class 2 !!!
It is of the form :
x + y + z = N
where x , y and z are integers and positive ones and N is a natural number.
Now its not that easy ....brainly is a app where no one can solve degree 3.
x^3+y^3+z^3=N
This is degree 3 .
If N is divisible by 3 then its easy to find a solution....just like baby feeding on milk-
If N is not divisible, then you will die in the bottom of the endless pit of equations and theories.
I am not like u.........I am a legend as discussed earlier.
So I will not die....I will kill everything......
Now :
x^3+y^3+z^3 may be divisible by 2
then switch one variable to 0 then do the magic....
But one problem :
If its a prime , then you are in trouble..
But its not a short tempered girlfriend ... you can get rid of that easily...
x^3+y^3+z^3=11 say
Then observe the following :
x can be 1 but that would make it 1 + y^3 + z^3 = 11
y^3 + z^3= 10 infact no solutions.
Hence there are very few prime solutions like this..
So infact you have to trial and error to get rid of this...
It is because very uniquely the equations will be made. ..
But if you fall into this one :
x / ( y + z ) + y / ( x + z ) + z / ( x + y ) = 4 then ??
Till now we were discussing about x^3+y^3+z^3 = N
If we had an equation of form :
x^3+y^3+z^3 + x^2y+xy^2+...............
Then obviously you cannot do this by trial and error dont be a fool.
Then you have to plot graphs.
Yupp 3 d graphs involving 3 diensions length breadth and height naming all variables x , y and z
Elliptic curves and graphs are not that easy..
Infact computers have to be used in certain cases.
And the fact that u need to take only positive coordinates is also tiring.
Maths is fun but when you go at the depth it will shake your foundations.
Variables are easy to find.
I will talk in the next episode about impossible and solution-less equations of degree 4
For today : bye
No one reads full answers in brainly....poof
Answer:
A third degree equation? What about any polynomial? To be honest, I’ll be rambling a bit, as I definitely know if I post it, it won’t receive any considerable views, and this is already a heavily followed question, which is answered 31 times before!
Normally, I’ll take the path of Vieta’s Formulae! Later, I will attempt (a minimum use of) Galois Theory. Finally, I will attempt to solve again the same polynomials with a special set of functions, which I consider the elementary functions of the non-elementary.
Also, this will probably be my (probably third) last answer in my polynomial series, maybe, and then I will focus on, probably, new stuff or the IMO.