# Why the results are different when use different letters?

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Xizeng Feng on 11 Mar 2022
Commented: Xizeng Feng on 14 Mar 2022
I solve same equations in different ketters and got fifferent results as follow:
But rs=a, xs=b, rp=c and xp=d. the equations are same!
>> syms rs xs rp xp;
>> [rp,xp]=solve(rs*rp^2+rs*xp^2==xp^2*rp,xs*rp^2+xs*xp^2==rp^2*xp)
rp =
-(rp*(rs*(rp - rs))^(1/2))/(rp - rs)
(rp*(rs*(rp - rs))^(1/2))/(rp - rs)
xp =
-(rs*(rp - rs))^(1/2)
(rs*(rp - rs))^(1/2)
-------------------------------------------------------------
>> syms a b c d
>> [c,d]=solve(a*c^2+a*d^2==c^2*d,b*c^2+b*d^2==d^2*c)
c =
0
(a^2 + b^2)/b
d =
0
(a^2 + b^2)/a

Walter Roberson on 12 Mar 2022
You are not specifying which two variables to solve for, so solve() is using symvar() and picking the first two variables.
With the different names involved, the relative order of the variables in symvar() is different than you are expecting.
Xizeng Feng on 13 Mar 2022
thank you very much for your kindly help. I learned more about the symbolic operations now.

DGM on 11 Mar 2022
They are not the same.
syms rs xs rp xp;
[rp,xp] = solve( rs*rp^2+rs*xp^2 == xp^2*rp, xs*rp^2+xs*xp^2 == rp^2*xp)
syms a b c d
[c,d] = solve( a*c^2+a*d^2 == c^2*d, b*c^2+b*d^2 == d^2*c)
The RHS of both equations don't correspond. You'll have to decide which one is which.
Xizeng Feng on 13 Mar 2022

Jan on 11 Mar 2022
Edited: Jan on 11 Mar 2022
Because the equations are different:
syms rs xs rp xp
syms a b c d
[rp, xp] = solve(rs * rp^2 + rs * xp^2 == xp^2 * rp, xs * rp^2 + xs * xp^2 == rp^2 * xp)
[c, d] = solve(a * c^2 + a * d^2 == c^2 * d, b * c^2 + b * d^2 == d^2 * c)
% ^ ?! ^
You see, the replacement is not performed exactly. The term xp is converted twice to c instead of d.
Xizeng Feng on 14 Mar 2022
Yes, I'll remember this point.