高考黑科技：我的解题思路震撼全球Zack00-著

小说简介

yiwanjiededoushishenghuoticaixiaoshuo《gaokaoheikeji：wodejietisiluzhenhanquanqiu》shi“zack00”deqingxinzhizuo，shuzhongzhurengongshiqinfenggaoyuan，xiaoshuogushijianshushi：∣pm∣⋅∣pn∣=∣−12−1(23)+12∣⋅2=∣−12−23+1∣⋅2=∣−3+4−66∣⋅2……

精彩章节

jiangtaishang，qinfengshouzhibanjiebaisefenbi，jingjingdizhulizaijudadeheibanqian。

yangguangtouguochuangling，zaitaqingshouquetingbadeshenyingshangtouxiayipianbanbodeguangyun，kongqizhong，xixiaodefenbichenaizaiguangzhuzhongfeiwu，rutongwushuweisuodexingchen。

zhenggegaosan（qi）ban，cikexianruleyizhongjinhuninggudesiji。

suoyourendemuguang，dourutongbeicishixiyindetiexie，laolaodidingzaiqinfengdeshenshang，yijitamianqianneidaokancheng“diyuji”nandudetuoyuanzonghedatishang。

xianqianneixiexingzailehuodeqiexiao、qingmiedeyilun、yijikanhaoxideyanshen，cikedouyiqiaoranyinqu，querdaizhide，shiyizhonghunzazhenanyizhixin、qiangliehaoqiyijiyisisimomingchengzhiwei“qidai”defuzaqingxu。

tamenshizaiwufalijie，zheigepingrililianjigexiandoumobudaode“zhumingxuezha”，jiujingshinalilaideyongqi，ganzaishuxuelaoshigaoyuandeshengnuyuquanbantongxuedezhushixia，rucicongrongbupodizoushangjiangtai，qutiaozhanyidaolianbanjidingjianxuebadouwangershengweidetimu？

nandaotazhendefengle？haishishuo，tayinzangleshenmebuweirenzhidemimi？

gaoyuanshuangshouhuanbaozaixiongqian，xieyizaijiangtaibianyuan，zuijiaoqinzheyimobinglengdejiqiao。tadaoyaokankan，zheigebuzhitiangaodihoudeqinfeng，jiujingnengzaizheidaotimumianqianchengduojiu！tashenzhiyijingxianghaole，dengqinfengzaiheibanqianzhuaernaosai、choutaibaichuzhihou，zijigairuheyongzuijiansuankebodeyuyan，jiangtaneikexiaode“zixin”chediniansui，rangtamingbaishenmejiaozuozhenzhengdejuewang！

qinfengmeiyoulihuizhouzaodeyiqie。

tadexinshen，yijingwanquanchenjinzaileyanqiandezheidaotimuzhizhong。

naohaizhong，“xueshenheikejixitong”defuzhugongnengyiqiaoranqidong。

【ding！jiancedaosuzhumianlingaonanduxueshutiaozhan，xitongfuzhumokuaiyijihuo。】

【“chujishuxuesiwei（suipian）”xiaoguozengqiang，luojituiyansudutisheng50%，fuzaxinxichulinenglitisheng30%！】

【zhengzaiduidangqiantimujinxingduoweidujiexi……jiexiwanbi！yiweisuzhushaixuanchuzuiyoujietilujingsantiao，qingsuzhuzixingxuanze。】

binglengerjixiedexitongtishiyin，rutongzuijingzhundedaohang，zaiqinfengdeyishishenchuxiangqi。

chaneijian，neidaoyuanbenzaitayanzhongyijiuxiandeyouxiepangencuojie、miwuzhongzhongdetuoyuandati，fangfobeiyizhiwuxingdedashoubokailecengcengmiwu，luchuleqineizaiqingxideluojimailuo。

gezhongxiangguandedingyi、dingli、gongshi、fuzhuxianzuofa、yijibutongjietisiludeyoulie，rutongchaoshuibanyongrutadenaohai，bingbeixunsuzhenghe、fenxi、youhua。

“yuanlairuci……”qinfengdeyanmoushenchu，shanguoyisilerandejingguang。

tashenxiyikouqi，ganshouzhedanaoqiansuoweiyoudeqingmingyuhuoyue，yijineiguyuanyu“chujishuxuesiwei”suipiande、duishuxuewentibenzhideminruidongchali。

然后，他动了。

shouzhongdefenbi，zaisuoyourendezhushixia，wenwendiluozaileheibandezuoshangjiao。

“唰——”

qingcuidemocashengxiangqi，dapolejiaoshineidesiji。

解：

yigeqingxieryoulide“jie”zi，rutongdianjingzhibi，shunjianxiyinlesuoyourendemuguang。

jinjiezhe，qinfengdebijiankaishizaiheibanshangfeiwuqilai。

（1）youtiyizhi，e=ca=22e=\frac{c}{a}=\frac{\sqrt{2}}{2}e=ac=22，zea2=2c2a^2=2c^2a2=2c2

youyinweia2=b2+c2a^2=b^2+c^2a2=b2+c2，suoyi$2c^2=b^2+c^2......zhixianpf2dexielv，zhixianpf₂dexielv，zhixianpf2dexielvk_{pf_2}=\frac{y}{x-c}。youk_{pf_1}\cdotk_{pf_2}=-\frac{1}{2}，de，de，de\frac{y^2}{(x+c)(x-c)}=-\frac{1}{2}，ji\frac{y^2}{x^2-c^2}=-\frac{1}{2}。yinweidianp(x,y)zaituoyuanshang，suoyi。yinweidianp(x,y)zaituoyuanshang，suoyi。yinweidianp(x,y)zaituoyuanshang，suoyi\frac{x^2}{a^2}+\frac{y^2}{b^2}=1，ji，ji，jiy^2=b^2(1-\frac{x^2}{a^2})。dairushangshi，bingjiehe。

dairushangshi，bingjiehe。dairushangshi，bingjieheb^2=c^2jijijia^2=2c^2de：\frac{c^2(1-\frac{x^2}{2c^2})}{x^2-c^2}=-\frac{1}{2}\frac{c^2-\frac{x^2}{2}}{x^2-c^2}=-\frac{1}{2}2(c^2-\frac{x^2}{2})=-(x^2-c^2)2c^2-x^2=-x^2+c^22c^2=c^2$

“ng？”qinfengxiedaozheili，meitouweiweiyicu。zheigejieguoxianranshicuowude。

taixia，gaoyuanzuijiaodejiqiaogengnongle：“zenme？zheijiukazhule？kanlai‘dashuxuejia’deshuipingyebuguorucima！”

yixietongxueyerenbuzhufachuledididechixiaosheng。

qinfengquehuangruoweiwen，tadedanaozaifeisuyunzhuan。xitongsuiranjichulezuiyoulujing，danjutidetuidaohejisuan，yiranxuyaotazijiwancheng。gangcaidetuidaoguochengzhong，xianranyouyigexijiebeitahulvele，huozheshuo，xitongjichude“xielvzhiji”zheigetiaojian，kenengyougengjianjiedeyingyongfangshi。

“dianpzaituoyuanshang，xielvzhiji……tuoyuandedierdingyi？

budui……dengdeng，y2=−12(x2−c2)y^2=-\frac{1}{2}(x^2-c^2)y2=−21(x2−c2)，zheigexingshi……”

qinfengdemuguangzaicisaoguotimutiaojian，naohaizhonglingguangyishan！

“我明白了！”

taxunsucadiaolegangcaituidaocuowudebufen，fenbijianzaicidianxiangheiban。

youkpf1-kpf2=−b2a2k_{pf_1}\cdotk_{pf_2}=-\frac{b^2}{a^2}kpf1⋅kpf2=−a**2shituoyuandeyigeguyouxingzhi（dangjiaodianzaixzhoushangshi，duiyufeidingdianp，qiyuliangjiaodianlianxianxielvzhijiweichangshu−b2a2-\frac{b^2}{a^2}−a**2）。

yinci，−b2a2=−12-\frac{b^2}{a^2}=-\frac{1}{2}−a**2=−21，jia2=**2a^2=**^2a2=**2。

......

suoyi，tuoyuancdebiaozhunfangchengwei：x22+y2=1\frac{x^2}{2}+y^2=12x2+y2=1

行云流水！

dangqinfengxiexiatuoyuanbiaozhunfangchengdeneiyike，taixianeixieyuanbenzhunbeikanxiaohuadetongxue，lianshangdebiaoqingdouweiweiyijiang。

suirandiyiwenxiangduijiandan，danqinfenggangcaineiduanzandetingdun、xunsudejiucuo、yijizuihouneiju“tuoyuandeguyouxingzhi”，douxianshichutaduituoyuanzhishidiandezhangwo，sihu……bingmeiyoutamenxiangxiangzhongneimebukan？

youqishineiju“guyouxingzhi”，henduotongxueshenzhidoumeitingshuoguo，huozhezhishizaimouxiecankaoshudejiaoluolijianguo，genbenmeidanghuishi！

gaoyuanyeshiweiweiyizheng，tameixiangdaoqinfengjingranzhidaozheigexiangduilengpidexingzhi。buguo，tahenkuaibianhuifulezhending，xinzhonglengxiao：“heng，waidazhengzhebale！diyiwensuannimenghunguoguan，wokannidierwen、disanwenzenmeban！”

qinfengmeiyoulihuitaixiadefanying，tadezhuyiligaodujizhong，fenbihaobutingxiedizhuanxiangledierwen。

（2）you（1）zhif1(−1,0),f2(1,0)f_1(-1,0),f_2(1,0)f1(−1,0),f2(1,0)。shezhixianldefangchengweix=my+1x=my+1x=my+1（dangzhixianlxielvkcunzaishi，m=1km=\frac{1}{k}m=k1；dangkbucunzaishi，zhixianlweix=1x=1x=1，yutuoyuanjiaoyu(1,±22)(1,\pm\frac{\sqrt{2}}{2})(1,±22)，cishiabzhongdianwei(1,0)(1,0)(1,0)jif₂，zhijing∣ab∣=2|ab|=\sqrt{2}∣ab∣=2，yuanxinweif₂，xianranbuguof₁，gukcunzaiqiebuwei0）。

jiangx=my+1x=my+1x=my+1dairutuoyuanfangchengx22+y2=1\frac{x^2}{2}+y^2=12x2+y2=1de：

......

shea(xa,ya),b(xb,yb)a(x_a,y_a),b(x_b,y_b)a(xa,ya),b(xb,yb)，zeya+yb=−2mm2+2y_a+y_b=-\frac{2m}{m^2+2}ya+yb=−m2+22m，yayb=−1m2+2y_ay_b=-\frac{1}{m^2+2}yayb=−m2+21。

yinweiyiabweizhijingdeyuanguodianf₁，suoyif1a⃗⋅f1b⃗=0\vec{f_1a}\cdot\vec{f_1b}=0f1a⋅f1b=0.

......

dairuweidadinglidebiaodashi：

(m2+1)(−1m2+2)+2m(−2mm2+2)+4=0(m^2+1)(-\frac{1}{m^2+2})+2m(-\frac{2m}{m^2+2})+4=0(m2+1)(−m2+21)+2m(−m2+22m)+4=0

......

suoyim=±7m=\pm\sqrt{7}m=±7

zezhixianldexielvk=1m=±17=±77k=\frac{1}{m}=\pm\frac{1}{\sqrt{7}}=\pm\frac{\sqrt{7}}{7}k=m1=±71=±77

“唰唰唰——”

fenbizaiheibanshanghuaguo，liuxiayixingxingqingxi、gongzheng、luojiyanmidetuiyanbuzhou。

qinfengdedongzuomeiyousihaodetingdun，fangfozheixiefuzadejisuanhetuidao，zaoyijingzaitanaohaizhongyanlianleqianbaibian。

tadesiluzhiqingxi，buzhouzhijianlian，suduzhikuaijie，yijingrangtaixiasuoyoudexueshengdoukandemudengkoudai！

neixieyuanbenhaidaizheyisiqingmiehehuaiyideyanshen，cikeyijingwanquanbeizhenjingsuoqudai！

“**！zhei……zheizhendeshiqinfengzaijieti？”

“tadesuduyetaikuaileba！erqiemeiyibudouhaoxiangmeiyoujingguosikaoyiyang，zhijiejiuxiechulaile！”

“dierwendejisuanliangzheimeda，tajingranyidiandoumeikaqiao？zheibukexuea！”

“nimenkantadebuzhou，yongxiangliangfachuliyuanguof₁detiaojian，silufeichangqingxi，biwomenpingshixiangdeneixieyingsuanyaojianjieduole！”

jiulianbanjilineijigezixuweixuebadexuesheng，cikeyeshimianmianxiangqu，congbicideyanzhongkandaoleyimonanyizhixindehairan。

tamenmenxinziwen，jiusuanbazheidaotijiaojitamenlaizuo，yejueduibukenengdadaoqinfengzheizhongjuzhongruoqing、xingyunliushuibandejingjie！

gaoyuanlianshangdejiqiaozaoyixiaoshidewuyingwuzong，querdaizhide，shiyizhongjianleguibandecuoeyudaizhi。

tadezuibaweiweizhangzhe，houjiebuzijuedishangxiahuadongleyixia，sihuxiangshuoxieshenme，quefaxianzijiyigeziyefabuchulai。

zhei……zheizenmekeneng？！

zheigeqinfeng，bushineigelianzuijichudetuoyuandingyidougaobuqingchudexuezhama？

tazenmekenengzairuciduandeshijiannei，ruciwanmeidijiechuzheidaotidedierwen？

nandao……tazhiqianyizhidouzaizangzhuo？

bu！bukeneng！gaoyuanlikefoudinglezheigehuangmiudexiangfa。tajiaoleqinfengliangnianduo，duitaneidiandizizaiqingchubuguole！

neizheidaodishizenmehuishi？！

gaoyuanganjuezijidedanaoyouxiedangji，yanqianfashengdeyiqie，yijingwanquanchaochuletaderenzhifanwei。

erqinfeng，duiyuzhouweineirutonghaixiaobanxiongyongdezhenjing，yijiuhuangruoweijue。

tadequanbuxinshen，douchenjinzaijietidelequzhizhong。

dangtaxiewandierwendedaan，fenbijianhaobutingxie，zhijiezhixiangleneinanduzuigao、yezuiweibiantaidedisanwen！

（3）you（2）zhi，zhixianldexielvk=77k=\frac{\sqrt{7}}{7}k=77(bufangquzhengzhi，lingyiqingkuangduicheng)。zem=7m=\sqrt{7}m=7

zhixianldefangchengweix=7y+1x=\sqrt{7}y+1x=7y+1

diana、bdezongzuobiaoshifangcheng((7)2+2)y2+27y−1=0((\sqrt{7})^2+2)y^2+2\sqrt{7}y-1=0((7)2+2)y2+27y−1=0ji$9y^2+2\sqrt{7}y-1=0delianggen。shedelianggen。shem(x_0,y_0)，ze\frac{x_0^2}{2}+y_0^2=1。zhixianmadefangchengwei。zhixianmadefangchengwei。zhixianmadefangchengweiy-y_a=\frac{y_0-y_a}{x_0-x_a}(x-x_a)。ling。lingx=4，ze，ze，zey_s=y_a+\frac{y_0-y_a}{x_0-x_a}(4-x_a)。tongli，y_t=y_b+\frac{y_0-y_b}{x_0-x_b}(4-x_b)。yaoqiu|os|\cdot|ot|=|y_s|\cdot|y_t|$(yinweis,tzaizhixianx=4shang，oweiyuandian，suoyi|os|=|ys|，|ot|=|yt|，zheilijiashes,tzaiyzhoutongce，ruoyicezexukaolvzhengfu，danzuizhongjieguoyingweidingzhi，anshikenengcunzaimouzhongduichengxinghuozheqiaomiaodehuajianshidefuhaowentibeixiaochuhuozhejieguoweipingfangshu)。

kandaozheili，taixiadexueshengmenyijingchedimamule。

qinfengdejietisudu，yijingkuaidaorangtamenliankanqingtimuhegenshangsiludougandaochili！

youqishidisanwen，neifuzadeshedian、lianlifangcheng、yijiduizhixianjiaodianzuobiaodebiaoda，guangshikanzhejiurangrentouyunmuxuan。

danqinfeng，quexiederutongtannangquwubanqingsongqieyi！

tadefenbizaiheibanshangtiaoyue，liuxiayigegejingzhuneryouyadeshuxuefuhao。tadeshentiweiweiqianqing，shenqingzhuanzhuerningjing，fangfozhenggeshijiezhishengxiatayuzheidaotimu。

zheiyikedeqinfeng，shenshangsanfazheyizhongnanyiyanyudeqiyimeili。

neizhongduizhishidejizhizhangkong，neizhongmianduinantishidecongrongzixin，neizhongchenjinzailixingsiweizhongdeduteqizhi，rangsuoyourendougandaoleyizhongyuanzilinghunshenchudezhenhan！

“zhei……zheihaishiwomenrenshideneigeqinfengma？”yigenvshengnannanziyu，shengyinzhongchongmanlebukesiyi。

“ta……tajianzhijiuxiangshihuanleyigeren！bu，shihuanleyigenaozi！”

“nandaotabeishenmexueshenfutilebucheng？”

gaoyuanyijingchedishuobuchuhualaile。tadaidaidizhanzaineili，kanzheqinfengzaiheibanshangneirutongshenlaizhibibandeyansuan，ganjuezijideshijieguanzhengzaibeiyidiandiandidianfu、zhongsu。

tayinyiweiaodejiaoxuejingyan，talaiyishengcundezhuanyequanwei，zaiqinfengzheifeiyisuosidebiaoxianmianqian，xiandeshirucidecangbaiwuli。

heibanshangdetuiyanhaizaijixu。

qinfengdesilurutongtianmaxingkong，queyoushizhongbuliluojideguidao。taqiaomiaodiyunyongledianzaituoyuanshangdecanshufangchengshefa，jieheleqicihuadesixiang，yijiyixiekansilengpidanqueyichanggaoxiaodejihexingzhi。

neixieyuanbenkanqilaiwubifanzadedaishushi，zaitashouzhong，rutongbeishilemofayiban，yibubudihuafanweijian，liuanhuaming。

……（cichushenglvenbujingweitianren、huafuxiuweishenqidetuidaoguocheng，yinweizuozheyexiebuchulai，danqingduzhezixingnaobuqiniubizhichu）……

zuizhong，jingguoyixilielingrenyanhualiaoluanqueyouluojiyanjindetuiyan，kede：

ysyt=(1-y02)(4−xa)(4−xb)−(y0−ya)(y0−yb)(x0−xa)(x0−xb)yixiefuzadankexiaoxiangdezuhe(x0−xa)(x0−xb)y_sy_t=\frac{(1-y_0^2)(4-x_a)(4-x_b)-(y_0-y_a)(y_0-y_b)(x_0-x_a)(x_0-x_b)

liyongxa=7ya+1,xb=7yb+1x_a=\sqrt{7}y_a+1,x_b=\sqrt{7}y_b+1xa=7ya+1,xb=7yb+1yijix02/2+y02=1x_0^2/2+y_0^2=1x02/2+y02=1dengtiaojianjinxingdaihuanhehuajian

kaolvdaoduichengxinghedingzhiwenti，keyichangshixunzhaoteshudianm，huozheliyonggenggaojidesheyingjihezhishi（suirangaozhongbuyaoqiu，dansilukeyijiejian）

yigegengjianjiedesilukenengshiliyongdingbidianchafahuozheyinrucanshufangchenghouliyongduichengxing

jingguojiankuzhuojuedansiluqingxidehuajian，zuizhongkeyizhengming：

∣ysyt∣=yigebuhanx0,y0dechangshu|y_sy_t|=\text{yigebuhan}x_0,y_0\text{dechangshu}∣ysyt∣=yigebuhanx0,y0dechangshu

（cichuqinfengdeshijijiefakenenggengweiqiaomiaohezhijie，liruliyonglemouzhongbianhuanhuozheteshudejihejielun，shidejisuanliangdafudujiangdi，zhanxianchuchaoyuechangguigaozhongshengshuipingdeshuxuesuyang）

zuizhong，qinfengzaiheibanshangxiexialejielun：

cunzaichangshuλ\lambdaλ，shide∣os∣⋅∣ot∣=λ|os|\cdot|ot|=\lambda∣os∣⋅∣ot∣=λhengchengli

jingguojisuan（cichushenglvelejutidejisuanguocheng，danqinfengdebanshushangqingxidizhanshilemeiyigebuzhou），kede：

λ=499\lambda=\frac{49}{9}λ=949。(cishuzhiweishili，shijiyinggenjutimuyanjintuidao)

“啪嗒。”

zuihouyibiluoxia，qinfengshouzhongdefenbiyeyinweiyonglierduanchengleliangjie，diaoluozaidishang，fachuleyishengqingweidecuixiang。

danzheishengqingxiang，querutongjingleiban，zaisijidejiaoshizhongzhaxiang！

qinfenghuanhuandizhuanguoshen，etoushangshenzheximidehanzhu，xiongtangyinweigangcaigaodujizhongdesikaoerweiweiqifu，dantadeyanshen，queyijiuqingcheermingliang，daizheyisijietihoudeshiranyudandandexiaoyi。

tapingjingdikanleyiyantaixianeixierutongbeishiledingshenfaban，yigegezhangdazuiba、dengyuanyanjing、manliandaizhidetongxue，zuihou，jiangmuguangtouxiangletongyangchuyushihuazhuangtaideshuxuelaoshigaoyuan。

“laoshi，zheidaoti，wojiewanle。”

tadeshengyinbugao，querutonghongzhongdalv，zaimeiyigerendeerbianhongranzuoxiang！

技惊四座！

zheiyike，zhenggegaosan（qi）ban，yaquewusheng！

suoyourendoubeiqinfengzheikanchengshenjibandebiaoxian，chedizhenshezhule！

neixingyunliushuibandejietiguocheng！

neiqingxiwubideluojisilu！

neikuaidaolingrenfazhideyansuansudu！

yijineizuizhongxiezaiheibanshangde、kanchengwanmeidedaan！

zheiyiqiedeyiqie，dourutongzuifenglidekedao，shenshendimingkezailemeiyigerendenaohaizhizhong，rangtamenyongshengnanwang！

gaoyuandaidaidikanzheheibanshangneimimimamaqueyoutiaoliqingxidetuiyanbuzhou，youkanlekanmianqianzheigeshenqingdanran、fangfozhishizuoleyijianweibuzudaoxiaoshideqinfeng，ganjuezijidehoulongxiangshibeishenmedongxiduzhule，yigeziyeshuobuchulai。

tadedanaoyipiankongbai，xinzhongzhishengxiawujindezhenhanyu……nanyizhixin！

zhei……zheizhendeshineigetayinxiangzhongwukejiuyaodexuezhaqinfengma？！

zheijiefa……zheisilu……zheisudu……

简直……太完美了！

wanmeidaorangtazheigejinyinshuxuejiaoxueshijiniandelaojiaoshi，dougandaozikuiburu！

tashenzhicongqinfengdejietibuzhouzhong，kandaoleyixietazijidouweicengxiangdaodeqiaomiaozhichu，yixiegengjianjie、genggaoxiaodechulifangfa！

zheiyike，gaoyuanganjuezijidelianjia**lade，xiangshibeirenhenhendichoulejishigeerguang！

tazhiqiandeneixiejifeng、neixiediaonan、neixieziyiweishideyouyuegan，zaicikeqinfengneinianyaxingdeshilimianqian，douxiandeshirucidekexiao，rucidebukanyiji！

“咕咚。”

buzhidaoshishei，jiannandiyanleyikoutuomo，dapolejiaoshineidesiji。

jinjiezhe，rutongliansuofanyingyiban，ciqibifudedaoxiliangqisheng、nanyizhixindejinghusheng、yijiyayibuzhudeyilunsheng，rutongchaoshuibanxiongyongerqi，shunjianyanmeilezhenggejiaoshi！

“tiana！wokandaoleshenme？qinfeng……qinfengtajingranzhendebazheidaotijiechulaile？！”

“erqie……erqiejiedezheimekuai！zheimewanmei！woliantimudoumeiwanquankanmingbaia！”

“zhei……zheibukeneng！zheijueduibukeneng！takendingshizuobile！huozhe……huozhetatiqiannadaotimule？”

“fangpi！gaolaotougangxiedetimu，tashangnaertiqiannaqu？erqienikantaneijietibuzhou，yiqihecheng，genbenbuxiangshibeide！”

“taiqiangle！zheizhendeshiqinfengma？tashenmeshihoubiandezheimeniubile？！”

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