三元二次方程组求解x的平方+y+z=3 x+1/2 y的平方+z=2 z的平方+1/3 x+z=1

[[x = -3*RootOf(81*_Z^8+324*_Z^7+162*_Z^6-630*_Z^5-423*_Z^4+522*_Z^3+175*_Z^2-208*_Z+38)^2-3*RootOf(81*_Z^8+324*_Z^7+162*_Z^6-630*_Z^5-423*_Z^4+522*_Z^3+175*_Z^2-208*_Z+38)+3, y = -9*RootOf(81*_Z^8+324*_Z^7+162*_Z^6-630*_Z^5-423*_Z^4+522*_Z^3+175*_Z^2-208*_Z+38)^4-18*RootOf(81*_Z^8+324*_Z^7+162*_Z^6-630*_Z^5-423*_Z^4+522*_Z^3+175*_Z^2-208*_Z+38)^3+9*RootOf(81*_Z^8+324*_Z^7+162*_Z^6-630*_Z^5-423*_Z^4+522*_Z^3+175*_Z^2-208*_Z+38)^2+17*RootOf(81*_Z^8+324*_Z^7+162*_Z^6-630*_Z^5-423*_Z^4+522*_Z^3+175*_Z^2-208*_Z+38)-6, z = RootOf(81*_Z^8+324*_Z^7+162*_Z^6-630*_Z^5-423*_Z^4+522*_Z^3+175*_Z^2-208*_Z+38)]]
这是我第一次见这么可怕的解。。
这是Algebraic Answer。。 RootOf就是当这个东西等于0的时候的值。。

这样的方程无法求解出具体的解，只能用软件找近似解，我特意花了点时间用matlab给你算了下，解有好几种，我把程序和解拷在下面，你自己对应看吧，x,y,z相同行对应的是一组
>> [x,y,z] = solve('x^2 + y + z = 3','x + 0.5*y^2 + z = 2','z^2+1/3*x+z=1')

x =

-2.1558096397175413208632102682324
2.3417683016658045479995603587582
-1.2694054456821613794740015901516
1.5697981332259246563154829507059
1.6611588330789069259700525786493
-0.59358614561699753216141747743743
1.3994819294241634717847593430704
-2.9534059663780993695712258953623


y =

-2.5505844145482914103793970728305
-1.2987433423594474975158583431781
3.1821070694215204544101697788912
1.8882207449206230289046359054338
-0.093882841658254402986456722184425
1.9443840933491424819684799922912
0.65629157310122349342520959953843
-3.7277928822265161478267831379616


z =

0.90306921184921609706913053220585
-1.1851354363272990742614441731111
-1.7934972549490472188215316354913
-1.3524869240002209253211014457879
0.33443417294217863986017055022295
0.70327139438241411947041541668009
0.38515875611399723798553159318324
-1.9948139200112388759811708379018

这个很难给出精确解,我能找到的数值近似解只有这些{x -> -3.04819,y -> -3.86614,z -> -2.42533},{x -> -1.74924,y -> -1.93567,z -> 1.87583},{x -> -0.741927 - 0.314823i,y -> 2.31845 + 0.593102 i,z -> 0.23021...