二次齐次式的应用

二次齐次式的应用 二次齐次式的应用 ,xy?????3?? ?3?i:22 axbxycy++(,,abc?u????),?????+?? ???]?????????r????/yx???i??,???????? ?)???????k.?8???u?????????I?????????? ??,?????????? sin tan cos y? y? y? =r,?????? c e a =r, ????2121 ()/()kyyxx=_o_o??,???3???3???i ?????+?I?????r.?)?????????s. ??1?? 22 1/2 log[2()1] xxx yaabb=+_o+ (,)abR+ _c,????y???;????x???????y??. ?a??_?01/21,0y<<<,?H?????????O ?I,??22 2()11xxx aabb+_o+>,?? 22 2()0xxx aabb+_o>.8? ???i?r?(?i???????u????x a??x b???? ?3???3?i,?8???/????2 (0)x b>?? 2 ()2()10xx aa bb +_o>. ???u???A????()xa b ?????3?.???i,???? ()21xa b >_o?k()21xa b <_o_o(?.??).8? ???u???A???????b???.???i,???????8 ?????? a b ??????????,?????a/1ab>,/1ab=, 0</1ab<?+??????????. ??0ab>>??,??1 a b >??, log(21)a b x>_o; ??0ab=>??,??/1ab=??,xR_c; ??0ab<<??,??0/1ab<<??, log(21)a b x<_o. ??????y?=_o,?[ 22 22 sin2sincoscos 4cos3sin1 y?y?y?y? y?y? _o_o _o+ ????????____. ?a???a?????i???a???D??4014<???n 22 sincosy?y?+,?[?????i???a???s?a???H?? ??siny??scosy??????3???3?i,???a?a??r,?a ????????2 cosy?,?[?????i?????ntany????i ??. ???i 22 22 sin2sincoscos 5cos2sin y?y?y?y? y?y? _o_o = _o 2 2 tan2tan11 52tan18 y?y? y? _o_o == _o .???? 1 18 . ??3?????????D???I???b????,?Q???Ix ???(,???????????Q???e??????3/5?????? ??????????Pr,Q?8??,??OPOQ_?,?e 4PQ=,?????????????). ?????????????)?? 222222 bxayab_o=,(I) ????PQ?????)??3/5()yxc=_o,?? 35 1 3 xy c _o =(???D22 cab=+).(II) ????(3?)r,(3?),???????3?k 222222235 [] 3 xy bxayab c _o _o=???a?? 22222 (53)() y abac x +_o 222222 215()330 y ababbc x +_o=. ???/OPr,OQ??????12 ,kk?????8??.?H OPOQ_??????????a?? 2222 2222 33 1 53 abbc abac _o =_o + . ?????a??2222 (3)(3)0abab_o+=,???? 22 3,2baca==,?a?B????(3?)r,(3?),???? y,??22 4490xaxa+_o= ??2 41PQPQ PQkxx==+_o 2 13/5()44PQPQ xxxxa=+_?+_o=. ???u1a=,???/2 3b=. ?????????????????)??22 /31xy_o=. ??4????????2 yx=??????O???8???? 22 2tan1/2 3?? ?????????QOAr,OB,???a?B??OAr,OB?? ???????a,???8?a???????k??????????C?? ???????). ?a????????AB?????)??1axby+=,?? ???????????)2 1yx_?=,???????3?k 2 ()yaxbyx+=,?????a?? 2 (/)(/)byxayx+_o10=,?[OAr,OB?? ????12 ,kk?????8??. ???HOAOB_??????????a??11/b_o=_o, ??1b=. ???/????AB???)??1axy+=,??AB?? ????(0,1)D,???HOAr,OB????????Ar,Cr, B????,?eOCAB_?,??OCCD_?,????C?? ?????u??OD?????????a: 22 (1/2)1/4xy+_o=(0)y_?. ??5????????2222 //1xayb_o=(0a<< )b?????Q????C,????l??(,0),(0,)ab?8??,?? ???????r????l????????3/4c,?[???????? ????????(). (A)2(B)3(C)2(D) 23 3 ??????l?????)??//1xayb+=, ??0bxayab+_o=. ?????rl???????? 22 003 4 ab c ab +_o = + , ?8??????r,????b,?????a,?? 4224 161630aacc_o+=, ?8???/????4 a,?? 24 1616(/)3(/)0caca_o+=, ????:2 c a =?k 23 3 c a =,?? 23 3 c a =, ?[ 224 3 ca=, 22221 3 bcaa=_o=,ba<,?? ?s????ab<????,?//2ca=?Q?c???i,???? 2e=,???+A. ???C??????????,ac?????3???3?i??e ????(?ke???y??)?u???????I????. ?t?????I?????D?????I ?????????????D???????; ?t???u???????+?O?i,???+???t????.?? ?????????+???s???????i??,?????????I?? ???????e?????????+??????,???.???I?e?? ?.???????????+?????????I,?I?e???<???? ?????????+???????????I.?C???H???????? ???????????????): 1?I?+?????ar,???????s?D?????I ??1?9?I?t?????????s???i: cos()coscossinsiny?y?y?y?y?y?_o=+. ???s??????,?I ?????a?D???t??OA uuur r, OB uuur ,?sx?????t???? ???a?B??y?r,y?,?[ ??A?????b?u(cos,y? sin)y?,??B?????b?u (cos,sin)y?y?,?[ coscossinsinOAOBy?y?y?y?_?=_o uuuruuur cos()OAOBy?y?=_?_?_o uuuruuur , _?cos()coscossinsiny?y?y?y?y?y?_o=+. ?I?t???????????????,r,???;?r?????? ??????.???I?/??????????????????r,???Q?? ?a,???????a,?+???????a,???????????????? ???a??????. 2?t?????I?????????D?????I ??2???s?+???????+????????????. ???s????2,??H??P?ABC?D?HAr,B?8 ??????????????????,,,HAxHByHCz=== uuurruuururuuurr , ?[AByx=_o uuururr ,BCzy=_o uuurrur ,CAxz=_o uuurrr ,?HHA ,BCHBAC_?_?????:()0xzy_?_o= rrur ,()yxz_?_o urrr 0=,?8?i????????:()0zxy_?_o= rrur , ??0zAB_o_?= ruuur ,????. ?I?t?????:?a ?????????D?????? ?????????+?????9 x y A O B A B 2 H C