-1
$\begingroup$

Is this number to big to work with

Solve 
[{x^2 + \
((17969491597941066732916128449573246156367561808012600070888918835531\
7264603414909334933722478686507552308558641999292218144366847228740520\
6525793749569434838926317115252252565441098081917061174250970244071801\
0364831638288518852689 + q^2)/
       q) x == -\
1796949159794106673291612844957324615636756180801260007088891883553172\
6460341490933493372247868650755230855864199929221814436684722874052065\
2579374956943483892631711525225256544109808191706117425097024407180103\
64831638288518852689, 

  x^2 + ((p^3 + 
         1796949159794106673291612844957324615636756180801260007088891\
8835531726460341490933493372247868650755230855864199929221814436684722\
8740520652579374956943483892631711525225256544109808191706117425097024\
40718010364831638288518852689 p)/
       p^2) x == \
-179694915979410667329161284495732461563675618080126000708889188355317\
2646034149093349337224786865075523085586419992922181443668472287405206\
5257937495694348389263171152522525654410980819170611742509702440718010\
364831638288518852689 , 

  x^2 + (p + q) x + 
    179694915979410667329161284495732461563675618080126000708889188355\
3172646034149093349337224786865075523085586419992922181443668472287405\
2065257937495694348389263171152522525654410980819170611742509702440718\
010364831638288518852689 == 0, Mod[p + q, 2] == 0}, {x, p, q}]
$\endgroup$
  • $\begingroup$ There is 4 equations with 3 unknowns... $\endgroup$ – mmeent May 3 '18 at 7:07
  • $\begingroup$ Anyway, evaluating this in 11.1.1 produces no errors. It just tells me there are no solutions. $\endgroup$ – mmeent May 3 '18 at 7:08
  • $\begingroup$ @mmeent is it bad to have 4 equation with 3 unknowns do I need another one, also I'm using 11.2 sorry for not letting putting it in $\endgroup$ – user546733 May 3 '18 at 7:26
0
$\begingroup$

You get imaginary solutions.

eqs1 = {x^2 + \
((17969491597941066732916128449573246156367561808012600070888918835531\
7264603414909334933722478686507552308558641999292218144366847228740520\
6525793749569434838926317115252252565441098081917061174250970244071801\
0364831638288518852689 + q^2)/
    q) x == -\
1796949159794106673291612844957324615636756180801260007088891883553172\
6460341490933493372247868650755230855864199929221814436684722874052065\
2579374956943483892631711525225256544109808191706117425097024407180103\
64831638288518852689, 
x^2 + ((p^3 + 
      179694915979410667329161284495732461563675618080126000708889\
1883553172646034149093349337224786865075523085586419992922181443668472\
2874052065257937495694348389263171152522525654410980819170611742509702\
440718010364831638288518852689 p)/
    p^2) x == \
-179694915979410667329161284495732461563675618080126000708889188355317\
2646034149093349337224786865075523085586419992922181443668472287405206\
5257937495694348389263171152522525654410980819170611742509702440718010\
364831638288518852689, 
x^2 + (p + q) x + 
 17969491597941066732916128449573246156367561808012600070888918835\
5317264603414909334933722478686507552308558641999292218144366847228740\
5206525793749569434838926317115252252565441098081917061174250970244071\
8010364831638288518852689 == 0};

Eliminate x and solve for p

sol1 = First@Solve[Eliminate[eqs1, x], p]

(*   {p ->1796949159794106673291612844957324615636756180801260007088891883\
5531726460341490933493372247868650755230855864199929221814436684722874\
0520652579374956943483892631711525225256544109808191706117425097024407\
18010364831638288518852689/q}   *)

sol2 = First@
  Solve[((p /. sol1) + q)/(k*2) == 0 && k \[Element] Integers, q]

(*   {q -> ConditionalExpression[-I \
\[Sqrt]179694915979410667329161284495732461563675618080126000708889188\
3553172646034149093349337224786865075523085586419992922181443668472287\
4052065257937495694348389263171152522525654410980819170611742509702440\
718010364831638288518852689, k \[Element] Integers && k != 0]}   *)

sol3 = Solve[eqs1 /. sol1 /. 
   Simplify[sol2, k \[Element] Integers && k != 0], x]

(*   {{x -> -I \
\[Sqrt]179694915979410667329161284495732461563675618080126000708889188\
3553172646034149093349337224786865075523085586419992922181443668472287\
4052065257937495694348389263171152522525654410980819170611742509702440\
718010364831638288518852689}, {x -> 
I \[Sqrt]\
1796949159794106673291612844957324615636756180801260007088891883553172\
6460341490933493372247868650755230855864199929221814436684722874052065\
2579374956943483892631711525225256544109808191706117425097024407180103\
64831638288518852689}}   *)

to get p, do

p /. sol1 /. sol2

Test

eqs1 /. sol1 /. sol2 /. sol3

(*   {{True, True, True}, {True, True, True}}   *)

Edit

to get all politive and negative solutions for x,p,q you better do

s3 = Solve[
       Flatten[{eqs1, {p + q == 0 || (p + q)/(2*k) == 0, 
 k \[Element] Integers, k != 0}}], {x, p, q}]

It shows, they are independent of k.

$\endgroup$
  • $\begingroup$ If i know there are suppose to be real solution, is there a way to readjust the equation to find that, and how come in your calculation you took out the Mod[p+q,2]==0 $\endgroup$ – user546733 May 3 '18 at 11:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.