MATLAB: Simultaneous equation’s answer with root(f(z),z,number)

answer with zroot(z)simultaneous equation

I wanna solve a simultaneous equation. (3variables and 3equations)
variables : x y la
 >> syms x y la
 >> [x y la]=solve(x^2/2+x-la+0.1==0, y^2/2+y-la==0, 1.0894*10^4/(1+x)+3.0426*10^5/(1+y)-560^2/1.1==0,[x y la])
Then the answer was
 la =
 root(z^4 + (19776924314555345282627381721241*z^3)/29985856331557066135916233922645 + (182550669846863552994267330435646073897117497002509261376288921*z^2)/3596606319747123967192837366359310876147667851420621775375184100 - (18048311478867063467883458941334406649252776520843039341675991*z)/899151579936780991798209341589827719036916962855155443843796025 + 414165676278263878346540653629150219301098208295051387892001/899151579936780991798209341589827719036916962855155443843796025, z, 1)
 root(z^4 + (19776924314555345282627381721241*z^3)/29985856331557066135916233922645 + (182550669846863552994267330435646073897117497002509261376288921*z^2)/3596606319747123967192837366359310876147667851420621775375184100 - (18048311478867063467883458941334406649252776520843039341675991*z)/899151579936780991798209341589827719036916962855155443843796025 + 414165676278263878346540653629150219301098208295051387892001/899151579936780991798209341589827719036916962855155443843796025, z, 2)
 root(z^4 + (19776924314555345282627381721241*z^3)/29985856331557066135916233922645 + (182550669846863552994267330435646073897117497002509261376288921*z^2)/3596606319747123967192837366359310876147667851420621775375184100 - (18048311478867063467883458941334406649252776520843039341675991*z)/899151579936780991798209341589827719036916962855155443843796025 + 414165676278263878346540653629150219301098208295051387892001/899151579936780991798209341589827719036916962855155443843796025, z, 3)
 root(z^4 + (19776924314555345282627381721241*z^3)/29985856331557066135916233922645 + (182550669846863552994267330435646073897117497002509261376288921*z^2)/3596606319747123967192837366359310876147667851420621775375184100 - (18048311478867063467883458941334406649252776520843039341675991*z)/899151579936780991798209341589827719036916962855155443843796025 + 414165676278263878346540653629150219301098208295051387892001/899151579936780991798209341589827719036916962855155443843796025, z, 4)
*similar answer forms for x and y as well.
Does that mean that it doesn't have a real solution?
If it does have a solution, could anyone explain me why this kind of solution happens and show me how I can get the correct answers???

Best Answer

Use the vpasolve function instead of solve:
syms x y la
[x y la] = vpasolve(x^2/2+x-la+0.1==0, y^2/2+y-la==0, 1.0894*10^4/(1+x)+3.0426*10^5/(1+y)-560^2/1.1==0,[x y la])
x =
    -1.0276526763938997599828120577753
   -0.98871345847551250957526212306944
    -1.9220361166774993145395788315577
   0.014826996444870776282293898407548
y =
   -0.55193229249169747712330616480155
    -1.4473559947285651166145007787567
   0.024768559459999792201312404153744
    0.10899676857658956985839980614832
la =
   -0.39961766474412712948313902214019
   -0.39993630699020800979779052473175
   0.025075300228861564800238254726083
    0.11493691635665888160170336870507
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