Seperate solutions from solution set

equation :

eqn1= tau + (6940736682536601*((40564819207303339226271666937215*((7958672037255683*tau)/211285985543901728)^(1/2))/40564819207303340847894502572032 - 24338891524382005378048193971515/81129638414606681695789005144064))/(4503599627370496*((100*((10371143640436539267540387993179*((7958672037255683*tau)/211285985543901728)^(1/2))/40564819207303340847894502572032 - 6222686184261924031538395930759/81129638414606681695789005144064)*((40564819207303339226271666937215*((7958672037255683*tau)/211285985543901728)^(1/2))/40564819207303340847894502572032 + 121694457621910018197126045574617/405648192073033408478945025720320))/(9*((40564819207303339226271666937215*((7958672037255683*tau)/211285985543901728)^(1/2))/40564819207303340847894502572032 - 4346557462141479/405648192073033408478945025720320)^2) - 6396823589615229/2251799813685248)*((8807500455112451*((7958672037255683*tau)/211285985543901728)^(1/2))/2251799813685248 - 5284500273067471/4503599627370496)) == 0

I got below answer after this command :simplify(solve(eqn1,tau))

tau ~= 86770006143284104137770088001067660899914768136/36315918750142936955822459988207044957384974699 & tau ~= (211285985543901728*((2^(1/2)*357313339412824509981525108943721604071071001084689465^(1/2)*1361129467683753853853498429727072845824i)/14095378286272805020446624941140030438778625454313157575975 - 1448852487380493/135216064024344464087572223124050)^2)/7958672037255683 & tau ~= (211285985543901728*((2^(1/2)*357313339412824509981525108943721604071071001084689465^(1/2)*1361129467683753853853498429727072845824i)/14095378286272805020446624941140030438778625454313157575975 + 1448852487380493/135216064024344464087572223124050)^2)/7958672037255683 & 563099457385191142840662871881142688341613012430*((7958672037255683*tau)/211285985543901728)^(1/2) + 365375409332725729550921208179070754913983135744*tau*((100*((10371143640436539267540387993179*((7958672037255683*tau)/211285985543901728)^(1/2))/40564819207303340847894502572032 - 6222686184261924031538395930759/81129638414606681695789005144064)*((40564819207303339226271666937215*((7958672037255683*tau)/211285985543901728)^(1/2))/40564819207303340847894502572032 + 121694457621910018197126045574617/405648192073033408478945025720320))/(9*((40564819207303339226271666937215*((7958672037255683*tau)/211285985543901728)^(1/2))/40564819207303340847894502572032 - 4346557462141479/405648192073033408478945025720320)^2) - 6396823589615229/2251799813685248)*((8807500455112451*((7958672037255683*tau)/211285985543901728)^(1/2))/2251799813685248 - 5284500273067471/4503599627370496) == 168929837215557355639015285929811462546538920515

there are 4 "&" symbols in the solution.

First Q1: does this mean, Is the first solution is :tau ~= 86770006143284104137770088001067660899914768136/36315918750142936955822459988207044957384974699.

I am expecting real and non -ve solution.after trying double(solve(eqn1,tau)) ,I got -ve and imaginary solutions.

Second Q2:If yes for first Q1, I tried to seperate using AND symbol after converting it into string ,then tried seperate first solution.then I am not able to convert it back numerical solution.

Could you please help.

Answer 1

[Ayush Gupta]

The solve function when used on eqn1 gives the following result as 3*1 symbolic table.

(211285985543901728*root(z^5 + (373359593908487267222143047811449852406397047099*z^4)/714549327259756936651062770353714189966575140864 - (9963400966170935713565782676544756915605254097742180546676602848293362482093379754424030677522172292040250319093*z^3)/3062121757193925444931997267043799011637238603433741914524424715305522666934101597267131075919872 + (29890202898512807144259261729678481392884246789538446809565750027578822996907944833124593257837350568132962338861*z^2)/30621217571939254449319972670437990116372386034337419145244247153055226669341015972671310759198720 + (561000993811838372282418673727435546046730341703538223700285867392791737986929061*z)/435153674117419405566237922335488834113055901786103435501392015582030505091509780480 - 6011176935019138052153154240987442970148590996828131503873955683/870307348234838811132475844670977668226111803572206871002784031164061010183019560960, z, 1)^2)/7958672037255683

(211285985543901728*root(z^5 + (373359593908487267222143047811449852406397047099*z^4)/714549327259756936651062770353714189966575140864 - (9963400966170935713565782676544756915605254097742180546676602848293362482093379754424030677522172292040250319093*z^3)/3062121757193925444931997267043799011637238603433741914524424715305522666934101597267131075919872 + (29890202898512807144259261729678481392884246789538446809565750027578822996907944833124593257837350568132962338861*z^2)/30621217571939254449319972670437990116372386034337419145244247153055226669341015972671310759198720 + (561000993811838372282418673727435546046730341703538223700285867392791737986929061*z)/435153674117419405566237922335488834113055901786103435501392015582030505091509780480 - 6011176935019138052153154240987442970148590996828131503873955683/870307348234838811132475844670977668226111803572206871002784031164061010183019560960, z, 3)^2)/7958672037255683

(211285985543901728*root(z^5 + (373359593908487267222143047811449852406397047099*z^4)/714549327259756936651062770353714189966575140864 - (9963400966170935713565782676544756915605254097742180546676602848293362482093379754424030677522172292040250319093*z^3)/3062121757193925444931997267043799011637238603433741914524424715305522666934101597267131075919872 + (29890202898512807144259261729678481392884246789538446809565750027578822996907944833124593257837350568132962338861*z^2)/30621217571939254449319972670437990116372386034337419145244247153055226669341015972671310759198720 + (561000993811838372282418673727435546046730341703538223700285867392791737986929061*z)/435153674117419405566237922335488834113055901786103435501392015582030505091509780480 - 6011176935019138052153154240987442970148590996828131503873955683/870307348234838811132475844670977668226111803572206871002784031164061010183019560960, z, 4)^2)/7958672037255683

Refer to the following code on how to get the solution:

syms tau;
eqn1 = tau + (6940736682536601*((7958672037255683*tau)/211285985543901728)^(1/2) - 20822210047609803/10)/(((8807500455112451*((7958672037255683*tau)/211285985543901728)^(1/2))/2251799813685248 - 5284500273067471/4503599627370496)*((4503599627370496*(((7958672037255683*tau)/211285985543901728)^(1/2) + 3/10)*((115142824613074125*((7958672037255683*tau)/211285985543901728)^(1/2))/4503599627370496 - 69085694767844475/9007199254740992))/(9*(((7958672037255683*tau)/211285985543901728)^(1/2) - 3477245969713183/324518553658426726783156020576256)^2) - 12793647179230458)) == 0;
sol = solve(eqn1, tau);

This should not give any & in the result. There are some more constraints which can be enforced by going through the documentation of solve here.