解一元三次方程x^3+x^2=1

解一元三次方程x^3+x^2=1
解一元三次方程
x^3+x^2=1

解一元三次方程x^3+x^2=1

答案：介于 0.7548776662 与 0.7548776663 之间.
其余两解为复数解:
x₂= -0.8774388331 + 0.7448617666i
x₃= -0.8774388331 - 0.7448617666i.
解法有很多种,尝试法不适用,牛顿法可以适用,下面用叠代法
任选一数,只要不是1,都可解答,现选 x.= 0.5
x³ + x² = 1
x₁= (1 - x².)^(⅓) = 0.9085602964
x₂= (1 - x²₁)^(⅓) = 0.5588306678
x₃= (1 - x²₂)^(⅓) = 0.8826762043
x₄= (1 - x²₃)^(⅓) = 0.6044873908
x5 = (1 - x²₄)^(⅓) = 0.8593410286
x6 = (1 - x²5 )^(⅓) = 0.6395023773
x7 = (1 - x²6 )^(⅓) = 0.8392116136
x8 = (1 - x²7 )^(⅓) = 0.6662370684
x9 = (1 - x²8 )^(⅓) = 0.8223530315
x10= (1 - x²9 )^(⅓) = 0.6866415893
x11= (1 - x²10)^(⅓) = 0.8085149479
x12= (1 - x²11)^(⅓) = 0.7022401560
x13= (1 - x²12)^(⅓) = 0.7973132595
x14= (1 - x²13)^(⅓) = 0.7141942878
x15= (1 - x²14)^(⅓) = 0.7883341060
x16= (1 - x²15)^(⅓) = 0.7233800293
x17= (1 - x²16)^(⅓) = 0.7811867390
x18= (1 - x²17)^(⅓) = 0.7304565099
x19= (1 - x²18)^(⅓) = 0.7755262674
x20= (1 - x²19)^(⅓) = 0.7359204588
x21= (1 - x²20)^(⅓) = 0.7710600334
x22= (1 - x²21)^(⅓) = 0.7401475387
x23= (1 - x²22)^(⅓) = 0.7675458045
x24= (1 - x²23)^(⅓) = 0.7434230494
x25= (1 - x²24)^(⅓) = 0.7647863727
x26= (1 - x²25)^(⅓) = 0.7459645804
x27= (1 - x²26)^(⅓) = 0.7626230032
x28= (1 - x²27)^(⅓) = 0.7479387282
x29= (1 - x²28)^(⅓) = 0.7609289534
x30= (1 - x²29)^(⅓) = 0.7494734840
x31= (1 - x²30)^(⅓) = 0.7596036119
x32= (1 - x²31)^(⅓) = 0.7506674668
x33= (1 - x²32)^(⅓) = 0.7585674505
x34= (1 - x²33)^(⅓) = 0.7515968483
x35= (1 - x²34)^(⅓) = 0.7577578060
x36= (1 - x²35)^(⅓) = 0.7523205798
x37= (1 - x²36)^(⅓) = 0.7571254206
x38= (1 - x²37)^(⅓) = 0.7528843583
x39= (1 - x²38)^(⅓) = 0.7566316441
x40= (1 - x²39)^(⅓) = 0.7533236524
x41= (1 - x²40)^(⅓) = 0.7562461911
x42= (1 - x²41)^(⅓) = 0.7536660207
x43= (1 - x²42)^(⅓) = 0.7559453557
x44= (1 - x²43)^(⅓) = 0.7539328925
x45= (1 - x²44)^(⅓) = 0.7557105972
x46= (1 - x²45)^(⅓) = 0.7541409426
x47= (1 - x²46)^(⅓) = 0.7555274234
x48= (1 - x²47)^(⅓) = 0.7543031522
x49= (1 - x²48)^(⅓) = 0.7553845122
x50= (1 - x²49)^(⅓) = 0.7544296315
x51= (1 - x²50)^(⅓) = 0.7552730215
x52= (1 - x²51)^(⅓) = 0.7545282570
x53= (1 - x²52)^(⅓) = 0.7551860480
x54= (1 - x²53)^(⅓) = 0.7546051664
x55= (1 - x²54)^(⅓) = 0.7551182031
x56= (1 - x²55)^(⅓) = 0.7546651435
x57= (1 - x²56)^(⅓) = 0.7550652816
x58= (1 - x²57)^(⅓) = 0.7547119176
x59= (1 - x²58)^(⅓) = 0.7550240019
x60= (1 - x²59)^(⅓) = 0.7547483959
x61= (1 - x²60)^(⅓) = 0.7549918037
x61= (1 - x²60)^(⅓) = 0.7547768452
x62= (1 - x²61)^(⅓) = 0.7549666894
x63= (1 - x²62)^(⅓) = 0.7547990330
x64= (1 - x²63)^(⅓) = 0.7549471008
x65= (1 - x²64)^(⅓) = 0.7548163376
x66= (1 - x²65)^(⅓) = 0.7549318222
x67= (1 - x²66)^(⅓) = 0.7548298339
x68= (1 - x²67)^(⅓) = 0.7549199055
x69= (1 - x²68)^(⅓) = 0.7548403600
x70= (1 - x²69)^(⅓) = 0.7549106108
x71= (1 - x²70)^(⅓) = 0.7548485696
x72= (1 - x²71)^(⅓) = 0.7549033614
x73= (1 - x²72)^(⅓) = 0.7548549726
x74= (1 - x²73)^(⅓) = 0.7548977072
x75= (1 - x²74)^(⅓) = 0.7548599665
x76= (1 - x²75)^(⅓) = 0.7548932972
x77= (1 - x²76)^(⅓) = 0.7548638615
x78= (1 - x²77)^(⅓) = 0.7548898576
x79= (1 - x²78)^(⅓) = 0.7548668993
x80= (1 - x²79)^(⅓) = 0.7548871748
x81= (1 - x²80)^(⅓) = 0.7548692686
x82= (1 - x²81)^(⅓) = 0.7548850824
x83= (1 - x²82)^(⅓) = 0.7548711166
x84= (1 - x²83)^(⅓) = 0.7548834505
x85= (1 - x²84)^(⅓) = 0.7548725579
x86= (1 - x²85)^(⅓) = 0.7548821776
x87= (1 - x²86)^(⅓) = 0.7548736820
x88= (1 - x²87)^(⅓) = 0.7548811849
x89= (1 - x²88)^(⅓) = 0.7548745588
x90= (1 - x²89)^(⅓) = 0.7548804106
x91= (1 - x²90)^(⅓) = 0.7548752426
x92= (1 - x²91)^(⅓) = 0.7548798067
x93= (1 - x²92)^(⅓) = 0.7548757759
x94= (1 - x²93)^(⅓) = 0.7548793357
x95= (1 - x²94)^(⅓) = 0.7548761919
x96= (1 - x²95)^(⅓) = 0.7548789683
x97= (1 - x²96)^(⅓) = 0.7548765163
x98= (1 - x²97)^(⅓) = 0.7548786818
x99= (1 - x²98)^(⅓) = 0.7548767694
x100=(1 - x²99)^(⅓) = 0.7548784583
x101=(1 -x²100)^(⅓) = 0.7548769667
x102=(1 -x²101)^(⅓) = 0.7548782840
x103=(1 -x²102)^(⅓) = 0.7548771207
x104=(1 -x²103)^(⅓) = 0.7548781481
x105=(1 -x²104)^(⅓) = 0.7548772407
x106=(1 -x²105)^(⅓) = 0.7548780420
x107=(1 -x²106)^(⅓) = 0.7548773344
x108=(1 -x²107)^(⅓) = 0.7548779593
x109=(1 -x²108)^(⅓) = 0.7548774074
x110=(1 -x²109)^(⅓) = 0.7548778949
x111=(1 -x²110)^(⅓) = 0.7548774644
x112=(1 -x²111)^(⅓) = 0.7548778445
x113=(1 -x²112)^(⅓) = 0.7548775088
x114=(1 -x²113)^(⅓) = 0.7548778053
x115=(1 -x²114)^(⅓) = 0.7548775434
x116=(1 -x²115)^(⅓) = 0.7548777747
x117=(1 -x²116)^(⅓) = 0.7548775705
x118=(1 -x²117)^(⅓) = 0.7548777508
x119=(1 -x²118)^(⅓) = 0.7548775915
x120=(1 -x²119)^(⅓) = 0.7548776322
x121=(1 -x²120)^(⅓) = 0.7548776608
x122=(1 -x²121)^(⅓) = 0.7548776177
x123=(1 -x²122)^(⅓) = 0.7548776208
x124=(1 -x²123)^(⅓) = 0.7548776064
x125=(1 -x²124)^(⅓) = 0.7548776308
x126=(1 -x²125)^(⅓) = 0.7548776976
x127=(1 -x²126)^(⅓) = 0.7548776386
x128=(1 -x²127)^(⅓) = 0.7548776907
x129=(1 -x²128)^(⅓) = 0.7548776447
x130=(1 -x²129)^(⅓) = 0.7548776853
x131=(1 -x²130)^(⅓) = 0.7548776494
x132=(1 -x²131)^(⅓) = 0.7548776811
x133=(1 -x²132)^(⅓) = 0.7548776531
x134=(1 -x²133)^(⅓) = 0.7548776778
x135=(1 -x²134)^(⅓) = 0.7548776560
x136=(1 -x²135)^(⅓) = 0.7548776753
x137=(1 -x²136)^(⅓) = 0.7548776583
x138=(1 -x²137)^(⅓) = 0.7548776733
x139=(1 -x²136)^(⅓) = 0.7548776600
x140=(1 -x²139)^(⅓) = 0.7548776717
x141=(1 -x²140)^(⅓) = 0.7548776614
x142=(1 -x²141)^(⅓) = 0.7548776705
x143=(1 -x²142)^(⅓) = 0.7548776625
x144=(1 -x²143)^(⅓) = 0.7548776696
x145=(1 -x²144)^(⅓) = 0.7548776633
x146=(1 -x²145)^(⅓) = 0.7548776689
x147=(1 -x²146)^(⅓) = 0.7548776639
x148=(1 -x²147)^(⅓) = 0.7548776683
x149=(1 -x²148)^(⅓) = 0.7548776645
x150=(1 -x²149)^(⅓) = 0.7548776678
x151=(1 -x²150)^(⅓) = 0.7548776648
x152=(1 -x²151)^(⅓) = 0.7548776675
x153=(1 -x²152)^(⅓) = 0.7548776652
x154=(1 -x²153)^(⅓) = 0.7548776672
x155=(1 -x²154)^(⅓) = 0.7548776654
x156=(1 -x²155)^(⅓) = 0.7548776667
x157=(1 -x²156)^(⅓) = 0.7548776656
x158=(1 -x²157)^(⅓) = 0.7548776668
x159=(1 -x²158)^(⅓) = 0.7548776657
x160=(1 -x²159)^(⅓) = 0.7548776667
x161=(1 -x²160)^(⅓) = 0.7548776658
x162=(1 -x²161)^(⅓) = 0.7548776666
x163=(1 -x²162)^(⅓) = 0.7548776659
x164=(1 -x²163)^(⅓) = 0.7548776665
x165=(1 -x²164)^(⅓) = 0.7548776666
x166=(1 -x²165)^(⅓) = 0.7548776665
x167=(1 -x²166)^(⅓) = 0.7548776661
x168=(1 -x²167)^(⅓) = 0.7548776664
x169=(1 -x²168)^(⅓) = 0.7548776661
x170=(1 -x²169)^(⅓) = 0.7548776664
x171=(1 -x²170)^(⅓) = 0.7548776661
x172=(1 -x²171)^(⅓) = 0.7548776663
x173=(1 -x²172)^(⅓) = 0.7548776662
x174=(1 -x²173)^(⅓) = 0.7548776663
x175=(1 -x²174)^(⅓) = 0.7548776662
x176=(1 -x²175)^(⅓) = 0.7548776663
x177=(1 -x²176)^(⅓) = 0.7548776662
x178=(1 -x²177)^(⅓) = 0.7548776663
x179=(1 -x²178)^(⅓) = 0.7548776662
x180=(1 -x²179)^(⅓) = 0.7548776663
x181=(1 -x²180)^(⅓) = 0.7548776662
x182=(1 -x²181)^(⅓) = 0.7548776663
x183=(1 -x²182)^(⅓) = 0.7548776662
x184=(1 -x²183)^(⅓) = 0.7548776663
x185=(1 -x²184)^(⅓) = 0.7548776662
x186=(1 -x²185)^(⅓) = 0.7548776663
.

x₁= 0.7548776662
x₂= -0.8774388331 + 0.7448617666i
x₃= -0.8774388331 - 0.7448617666i。