【“guomubuwang（tiyanban）”yiqidong，chixushijian：59fen59miao。】
binglengerjingzhundedaojishisheng，rutongzhangubanzaiqinfengdenaohaizhongleixiang。
neiyishunjian，qinfengganjuezijidedanaofangfobeiyidaowuxingdedianliuchuanguo，zhenggeshijiezaitadeganzhizhongshunjianbiandebutong！
yanqiandekezhuo，muwendemeiyisixiweizouxiangdouqingxiderutongdaoke；kongqizhongpiaofudeweichen，zaitouguochuanglingdeyangguangxia，qiyundongguijidoufangfobeifangmanlewushubei，lilizaimu。tadeerduonengbuzhuodaojiaoshiwaizoulangshangqitabanjilaoshijiangkedemohushengyin，shenzhinengfenbianchugebibanhuaxuelaoshineidutedeshayasangyin。
gengrangtagandaozhenhandeshitadesiwei。
ruguoshuozhiqiandenaodaishiyitailaojiudebentengdiannao，yunxinggesaoleidoukadun，neimexianzai，tajiuxiangshishunjianshengjichenglezuidingjiandeliangzijisuanji！siweideyunzhuansudu、qingxidu、yijiduixinxidebuzhuohechulinengli，doudadaoleyigetayiwangxiangdoubuganxiangdekongbujingdi！
“zheijiushi……guomubuwang？”qinfengnannanziyu，yanzhongshanshuozhenanyizhixindeguangmang。
tameiyousihaoyouyu，jihushibennengdi，yibazhuaguozhuomianshangneibenzhanxinde、jihumeizenmefandongguode《gaozhongshuxuebixiuwu》，yijipangbianduijirushande《wuniangaokaoxnianmoni》、《huangxmijuan》、《xuebabiji》denggezhongfuxiziliao。
zheixiecengjingzaitayanzhongrutongtianshuyibandecunzai，cike，quesanfazheqiansuoweiyoudexiyinli。
“shijianzhiyouyixiaoshi！”qinfengshenxiyikouqi，qiangyaxiaxinzhongdejidang，muguangruiliruyingsun。
tashouxianjiangneidaoxitongfabude、haocheng“gaokaoyazhoutijibie（lveyouchaogang）”defuzahanshuti，shenshendiluoyinzainaohaizhong。meiyigefuhao，meiyigejiaobiao，meiyigetiaojian，douzai“guomubuwang”dejiachixia，beiwanmeifuke，fenhaobucha。
jinjiezhe，tafankaile《gaozhongshuxuebixiuwu》。
“唰唰唰——”
shuyefandongdeshengyinzaianjingdejiaoluolixiandegewaiqingxi。
qinfengdemuguangrutongzuijingmidesaomiaoyi，feisudilveguoshuyeshangdemeiyigezi、meiyigegongshi、meiyigeliti。
neixiecengjingrangtatoutongyulie、baisibudeqijiededingyi、dingli、tuilun，cikerutongwenshundemianyangban，guaiguaidiyongrutadenaohai，bingqiebeixunsuguilei、zhengli、jiyi。
“yuanlaihanshudedandiaoxingshizheimepanduande……”
“daoshudejiheyiyi……zhiqianzenmejiumeilijietoucheni？”
“zheigeluobidafaze，shushangjingranyoutidao！suiranzhishizaituozhanyueduli……”
wushucengjingmohubuqing、huozhegancuijiumeikanjinqudezhishidian，zai“guomubuwang”dekongbuxiaoguoxia，beitayiyizhongcuikulaxiubandesuduqiangxingjiyibingchubulijie。
tadedanaoxiangyikuaiganhedehaimian，fengkuangdixishouzhezhishideganlin。
duanduanshifenzhong，yibenhouhoude《bixiuwu》hexinneirong，jingranbeitahuluntunzaoban“ken”lexialai！suiranhenduoshencengcideluojiguanliantaweibinenglikeronghuiguantong，danzhishao，suoyoudegongshi、dinglihejibenjietibuzhou，tadoujideyiqingerchu！
这种感觉，太爽了！
jianzhijiuxiangshiwuxiaxiaoshuolidezhujiaobeidatonglerenduermai，xueshenmedoushiyidianjiutong！
qinfengshenzhinengqingxidiganjuedao，suizhezhishideyongru，taneiganggangtishengdao7diandezhili，zhengzaibeiyouxiaodiliyongqilai，bangzhutaduizheixieqiangxingjiyixialaidexinxijinxingchubudexiaohuaheshuli。
tameiyoutingxie，jinjiezheyouzhuaqile《wuniangaokaoxnianmoni》zhongguanyuhanshuyudaoshudebufen。
hailiangdetixing，gezhongdiaozuandekaofa，wuhuabamendejietijiqiao……
ruoshicongqian，guangshikandaozheixiemimimamadetimu，qinfengkongpajiuyijingtoupifama，zhijiexuanzefangqile。
danxianzai，taquekandejinjinyouwei，shenzhiyouxieruchiruzui。
meiyidaoti，zaitayanzhongdouxiangshiyigedengdaibeijiekaidemiti。tafeisudiyuedutimu，ranhouduizhaodaanjiexi，jianggezhongjietisilu、guanjianbuzhou、yicuodian，yiyimingjizaixin。
“yuanlaizheidaotikeyiyonggouzaohanshudefangfa……”
“zheigecanshufenlifa，yongzaizheilizhenshiqiaomiao！”
“haiyouzheizhonghuanyuanjiqiao，woyiqianzenmejiumeixiangdao？”
tadeetoushangshenchuleximidehanzhu，bushiyinweilei，ershiyinweidanaogaosuyunzhuandailaidexingfen。tadeyanshenzhuanzhuermingliang，fangfoyouliangtuanhuoyanzairanshao。
shijianyifenyimiaodiliushi。
sishifenzhonghou，qinfengjihujiangshoutousuoyouyuhanshu、daoshu、budengshi、jiexijihexiangguandehexinzhishidianhedianxingtixing，douyong“guomubuwang”denengliqiangxing“sai”jinlenaozili。
tadedanaocikejiuxiangyigebeisaimanledingjishicaidechaojibingxiang，suiranhenduodongxihaimeilaideji“pengrenxiaohua”，danzhishao，“yuancailiao”yijingchubeidaoleyigejingrendedibu！
【“guomubuwang（tiyanban）”shengyushijian：19fen37miao。】
xitongdetishiyinshishixiangqi。
“shijianbuduole，gaijiejueneidao‘lanluhu’le！”qinfengmuguangyining，jiangsuoyoukebenhexiticetuidaoyibian，shenxiyikouqi，zhongxinjiangzhuyilijujiaodaoneidaoxitongfabudeshuxuenantishang。
neishiyidaoyituoyuanweibeijing，jiehelehanshu、daoshu、budengshizhengmingyijicanshufanweitantaodechaojizonghedati。timutiaojianfanfu，shewencengcengdijin，jisuanlianghesiweiliangdoujiqikongbu。
ruoshisishifenzhongqian，qinfengkandaozheidaoti，kongpaliantimudoudubumingbai，gengbietijietile。
danxianzai，dangtazaicishenshizheidaotimushi，ganjuequejieranbutong。
neixiecengjingrutongluanmabandeshuxuefuhaohezhuanyeshuyu，cikezaitayanzhong，doubiandeqingximingle。tashenzhinengcongneirongzhangdetiganzhong，xunsubolichuhexindeyizhitiaojianhedaiqiuwenti。
“diyiwen，qiutuoyuancdebiaozhunfangcheng……zheigejiandan，liyonglixinlvhedianzaituoyuanshang，lianlifangchengzujike。”
qinfengdesiluyichangqingxi，naqibi，zaicaogaozhishangfeikuaidiyansuanqilai。
e=ca=22e=\frac{c}{a}=\frac{\sqrt{2}}{2}e=ac=22
x02a2+y0**2=1\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}=1a2x02+b2y02=1
a2=b2+c2a^2=b^2+c^2a2=b2+c2
jigejichugongshizaitanaohaizhongzidongfuxian，dairutimujichudejutishuzhi，yixilieyunsuanxingyunliushui。
“a²=2，b²=1。suoyituoyuancdefangchengwei：x22+y2=1\frac{x^2}{2}+y^2=12x2+y2=1。”
jinjinliangfenzhong，diyiwenbianbeitaqingsongnaxia。
“dierwen，shezhixianlyutuoyuancjiaoyua,bliangdian，ruodianp(1,1/2)manzupaxiangliang+pbxiangliang=0xiangliang，qiuzhixianldexielvk。”
“pa+pb=0，yiweizhepshiabdezhongdian。liyongdianchafahuozheweidadingli……”
qinfengdebijianzaicaogaozhishangfeiwu，gezhongjietifangfazaitanaohaizhongshanxian，bingbeixunsushaixuanchuzuiyoulujing。
shezhixianldefangchengweiy−12=k(x−1)y-\frac{1}{2}=k(x-1)y−21=k(x−1)，dairutuoyuanfangcheng，xiaoquy，dedaoyigeguanyuxdeyiyuanercifangcheng。
(1+2k2)x2−(4k2−2k)x+(2k2−2k−32)=0(1+2k^2)x^2-(4k^2-2k)x+(2k^2-2k-\frac{3}{2})=0(1+2k2)x2−(4k2−2k)x+(2k2−2k−23)=0
liyongweidadinglixa+xb=4k2−2k1+2k2x_a+x_b=\frac{4k^2-2k}{1+2k^2}xa+xb=1+2k24k2−2k。
yinweipshiabzhongdian，suoyixp=xa+xb2=1x_p=\frac{x_a+x_b}{2}=1xp=2xa+xb=1。
4k2−2k2(1+2k2)=1\frac{4k^2-2k}{2(1+2k^2)}=12(1+2k2)4k2−2k=1
jiezheigeguanyukdefangcheng，dedaok=−1k=-1k=−1。
“dierwen，k=-1，yejiejuele！”qinfengdezuijiaobuzijuedigouqiyimoxiaorong。
zheizhonggongkenantide**，shitayiqiancongweitiyanguode！
zhenzhengdetiaozhan，shidisanwen。
“disanwen，zaidierwendetiaojianxia，guodianpzuozhixianmchuizhiyul，jiaotuoyuancyum,nliangdian。shiwenshifoucunzaiyigechangshuλ，shide|pm|·|pn|=λ|pa|·|pb|hengchengli？ruocunzai，qiuchuλdezhi；ruobucunzai，shuomingliyou。”
zheiyiwen，shejixianzhanggongshi、xiangliangmozhang、yijihengchengliwenti，jisuanlianghesiweinandudoudourantishenglehaojigedangci。
qinfengdemeitouweiweicuqi。
tanengganjuedao，zheiyiwendenandu，yijingchaochuletaganggangqiangxingjiyixialaideneixie“taolu”suonengzhijiejiejuedefanchou。taxuyaogengshencengcidelijiehegenglinghuodeyunyong。
“lengjing……zixifenxi……”qinfengbishangyanjing，naohaizhongganggang“tun”xiaqudewushuzhishidianrutongxingchenbanshanyao。
zhixianldexielvwei-1，zezhixianmdexielvwei1。
zhixianmdefangchengweiy−12=1(x−1)y-\frac{1}{2}=1(x-1)y−21=1(x−1)，jiy=x−12y=x-\frac{1}{2}y=x−21。
jiangzhixianmdefangchengdairutuoyuanfangchengx22+y2=1\frac{x^2}{2}+y^2=12x2+y2=1，dedaoguanyuxdeyiyuanercifangcheng：
x22+(x−12)2=1\frac{x^2}{2}+(x-\frac{1}{2})^2=12x2+(x−21)2=1
x22+x2−x+14=1\frac{x^2}{2}+x^2-x+\frac{1}{4}=12x2+x2−x+41=1
32x2−x−34=0\frac{3}{2}x^2-x-\frac{3}{4}=023x2−x−43=0
6x2−4x−3=06x^2-4x-3=06x2−4x−3=0
shem(x₁,y₁)，n(x₂,y₂)，zex1+x2=46=23x_1+x_2=\frac{4}{6}=\frac{2}{3}x1+x2=64=32，x1x2=−36=−12x_1x_2=-\frac{3}{6}=-\frac{1}{2}x1x2=−63=−21。
∣pm∣⋅∣pn∣=(x1−xp)2+(y1−yp)2⋅(x2−xp)2+(y2−yp)2|pm|\cdot|pn|=\sqrt{(x_1-x_p)^2+(y_1-y_p)^2}\cdot\sqrt{(x_2-x_p)^2+(y_2-y_p)^2}∣pm∣⋅∣pn∣=(x1−xp)2+(y1−yp)2⋅(x2−xp)2+(y2−yp)2
youyudianm,nzaizhixiany=x−12y=x-\frac{1}{2}y=x−21shang，qiep(1,1/2)yezaizheitiaozhixianshang（yinweizhixianmguopdian），suoyipmhepndebiaodashikeyijianhua。
shijishang，pshixianmnshangdeyigedingdian。
∣pm∣⋅∣pn∣=∣(x1−xp)(x2−xp)∣⋅(1+km2)|pm|\cdot|pn|=|(x_1-x_p)(x_2-x_p)|\cdot(1+k_m^2)∣pm∣⋅∣pn∣=∣(x1−xp)(x2−xp)∣⋅(1+km2)，zheilikm=1k_m=1km=1。
∣pm∣⋅∣pn∣=∣x1x2−xp(x1+x2)+xp2∣⋅(1+12)|pm|\cdot|pn|=|x_1x_2-x_p(x_1+x_2)+x_p^2|\cdot(1+1^2)∣pm∣⋅∣pn∣=∣x1x2−xp(x1+x2)+xp2∣⋅(1+12)
∣pm∣⋅∣pn∣=∣−12−1(23)+12∣⋅2=∣−12−23+1∣⋅2=∣−3+4−66∣⋅2=∣−16∣⋅2=13|pm|\cdot|pn|=|-\frac{1}{2}-1(\frac{2}{3})+1^2|\cdot2=|-\frac{1}{2}-\frac{2}{3}+1|\cdot2=|-\frac{3+4-6}{6}|\cdot2=|-\frac{1}{6}|\cdot2=\frac{1}{3}∣pm∣⋅∣pn∣=∣−21−1(32)+12∣⋅2=∣−21−32+1∣⋅2=∣−63+4−6∣⋅2=∣−61∣⋅2=31。
zheigejisuanguocheng，qinfengxiedejiweiliuchang。
jiexialaishijisuan|pa|·|pb|。
zhixianldefangchengweiy−12=−1(x−1)y-\frac{1}{2}=-1(x-1)y−21=−1(x−1)，jiy=−x+32y=-x+\frac{3}{2}y=−x+23。
dairutuoyuanfangchengx22+y2=1\frac{x^2}{2}+y^2=12x2+y2=1：
x22+(−x+32)2=1\frac{x^2}{2}+(-x+\frac{3}{2})^2=12x2+(−x+23)2=1
x22+x2−3x+94=1\frac{x^2}{2}+x^2-3x+\frac{9}{4}=12x2+x2−3x+49=1
32x2−3x+54=0\frac{3}{2}x^2-3x+\frac{5}{4}=023x2−3x+45=0
6x2−12x+5=06x^2-12x+5=06x2−12x+5=0
shea(x₃,y₃)，b(x₄,y₄)，zex3+x4=126=2x_3+x_4=\frac{12}{6}=2x3+x4=612=2，x3x4=56x_3x_4=\frac{5}{6}x3x4=65。
tongyang，p(1,1/2)shixianabdezhongdian。
∣pa∣⋅∣pb∣=∣(x3−xp)(x4−xp)∣⋅(1+kl2)|pa|\cdot|pb|=|(x_3-x_p)(x_4-x_p)|\cdot(1+k_l^2)∣pa∣⋅∣pb∣=∣(x3−xp)(x4−xp)∣⋅(1+kl2)，zheilikl=−1k_l=-1kl=−1。
youyupshiabzhongdian，suoyixp=x3+x42x_p=\frac{x_3+x_4}{2}xp=2x3+x4，zheiyiweizhex3−xp=−(x4−xp)x_3-x_p=-(x_4-x_p)x3−xp=−(x4−xp)。
yinci，∣pa∣⋅∣pb∣=∣pa∣2=(x3−xp)2(1+kl2)|pa|\cdot|pb|=|pa|^2=(x_3-x_p)^2(1+k_l^2)∣pa∣⋅∣pb∣=∣pa∣2=(x3−xp)2(1+kl2)。
x3,x4x_3,x_4x3,x4shifangcheng$6x^2-12x+5=0delianggegen。panbieshidelianggegen。panbieshidelianggegen。panbieshi\delta=(-12)^2-4\cdot6\cdot5=144-120=24＞0。。。x_{3,4}=\frac{12\pm\sqrt{24}}{12}=1\pm\frac{2\sqrt{6}}{12}=1\pm\frac{\sqrt{6}}{6}。suoyi，。suoyi，。suoyi，x_3=1-\frac{\sqrt{6}}{6}，，，x_4=1+\frac{\sqrt{6}}{6}(huoxiangfan，buyingxiangjieguo)。(huoxiangfan，buyingxiangjieguo)。(huoxiangfan，buyingxiangjieguo)。|x_3-x_p|=|1-\frac{\sqrt{6}}{6}-1|=\frac{\sqrt{6}}{6}。。。|pa|^2=(\frac{\sqrt{6}}{6})^2(1+(-1)^2)=\frac{6}{36}\cdot2=\frac{1}{6}\cdot2=\frac{1}{3}。suoyi，。suoyi，。suoyi，|pa|\cdot|pb|=\frac{1}{3}$。
“ng？|pm|·|pn|=1/3，|pa|·|pb|=1/3？”
qinfengkanzhecaogaozhishangdejieguo，yanzhongshanguoyisimingwu。
“ruguo|pm|·|pn|=λ|pa|·|pb|hengchengli，neimeλ=1？”
tazixijianchaleyibianzijidejisuanguocheng，meiyigebuzhoudouqingxiwuwu。
“guomubuwang”dailaidebujinjinshijiyili，haiyouyizhongduixijiedejizhidongchali，rangtahennanzaijisuanzhongchucuo。
ernei7diandezhili，suiranbugao，danzaicikeyefahuileguanjianzuoyong，rangtadeluojituilinenglishangleyigexiaotaijie。
【“guomubuwang（tiyanban）”shengyushijian：02fen15miao。】
时间所剩无几！
qinfengetouyijingbumanlehanzhu，dantayanshenqueyuelaiyueliang。
taxunsuzhenglisilu，jiangzhenggejietiguochengqingxi、wanzhengdishuxiezailingyizhangganjingdecaogaozhishang。zijisuiranyinweizhuiqiusuduerlvexianliaocao，danmeiyigebuzhoudoutiaoliqingxi，luojiyanjin。
dangtaxiexiazuihouyige“zongshangsuoshu，cunzaichangshuλ=1，shidedengshihengchengli”dejielunshi，naohaizhongdedaojishi，zhenghaotiaodaole“00fen03miao”。
“呼——”
qinfengzhangzhangdishuleyikouqi，zhenggerenrutongxutuoyiban，kaozaileyibeishang。
jihuzaitongshi，neizhongdanaorutongchaojijisuanjibangaosuyunzhuan、duiyiqiexinxiguomubuwangdeqiyiganjue，chaoshuibantuiqu。
tadedanaohuifulewangchangdezhuangtai，shenzhiyinweigangcaidechaofuheyunzhuan，haidaizheyisiqingweidepibeiheyunxuan。
dantaxinzhong，quechongmanleqiansuoweiyoudechongshiganhexiyue！
他做到了！
tajingranzhendedulijiejueleyidaoliantazijidoubuganxiangxiangdechaojinanti！
zheizhongtongguozishennuli（suiranyouxitongfuzhu）gongkenanguansuodailaidejudachengjiugan，shirenhedongxidouwufabinide！
xuexi，yuanlaiyekeyizheimeshuang！
jiuzaizheishi，binglengjixiedexitongtishiyin，ruyueerzhi：
【ding！xinshourenwu：dulizhengquejiedashuxuenanti，yiwancheng！】
【renwupingjia：youxiu（jietisiluqingxi，buzhouwanzheng，yongshi57fen57miao，fuheyuqi）。】
【zhengzaijiesuanrenwujiangli……】
qinfengdexinzangbuzhengqidijiasutiaodongqilai，yanzhongchongmanleqidai。
【gongxisuzhuhuodejiangli：10dianxueshenjifen！】
【gongxisuzhuhuodejiangli：“chujishuxuesiwei”（suipian1/3）！】
10点学神积分！
qinfengdeyanjingshunjianliangle！
zaizhiqiandexitongjieshaozhong，tayinyuejide，jifensihushixitongshangchenglideyingtonghuo，keyiyonglaiduihuangezhongshenqidedaojuhenengli！zheikeshishidashidehaodongxi！
ergengrangtajingxide，shineige“chujishuxuesiwei”suipian！
jiuzaixitongtishiyinluoxiadeshunjian，qinfengganjuedaoyiguweiruodanqueyichangxuanmiaodenuanliu，congzijimeixinchuyongrudanao。
jinjiezhe，tanaohaizhongguanyushuxuedeneixielingsande、tongguo“guomubuwang”qiangxingjiyixialaidezhishidian，fangfobeiyizhiwuxingdedashouqingqingbodongleyixia。
xuduozhiqianzhishijizhudanbingweiwanquanlijietouchedegongshidingli，cikejingranyouleyizhonghuorankailangdeganjue！
taduiganggangjiechudeneidaofuzahanshuti，yeyoulegengshenyicengdeganwu。
ruguorangtaxianzaizhongxinzuoyibian，tashenzhinengyinyueganjuedao，chulezijigangcaiyongdeneizhongjiefawai，sihuhaiyouqitagengjianjie、gengqiaomiaodesilu！
zheizhongganjuefeichangqimiao，jiuxiangshiyuanbenhundunyipiandeshuxueshijie，turanbeidianliangleyizhanxiaoxiaodemingdeng，suiranguangmangweiruo，quezuyizhaoliangyixiaopianquyu，rangtaduishuxuedeganzhihelijie，doutishengleyigeweixiaodecengci。
“zheijiushi‘chujishuxuesiwei’suipiandexiaoguoma？”qinfengxinzhongzhenhan。
jinjinshisanfenzhiyidesuipian，jiuyourucixiaoguo，neiruoshijiqilewanzhengde“chujishuxuesiwei”，shenzhishigenggaojideshuxuesiwei，neizijiqibushizhendenengchengweishuxuezhishen？
xitongdeshenqiheqiangda，zaiyicishuaxinletaderenzhi。
taditoukanlekanzijiyinweizhangshijianyongliwobieryouxiefahongdeshouzhi，youkanlekanneizhangxiemanletuiyanguochengdecaogaozhi。
suiran“guomubuwang”dexiaoguoyijingxiaoshi，dangangcaineiyigexiaoshidefengkuangxuexihejietiguocheng，queshenshendiluoyinzailetadejiyizhong。neixiebeita“tun”xiaqudezhishi，bingmeiyouwanquanxiaoshi，ershiyouyibufen，zaita7dianzhilihe“chujishuxuesiwei”suipiandeyingxiangxia，zhenzhengkaishichendianxialai，zhuanhuaweitazijidedongxi。
“xueshenheikejixitong……”qinfengdeyanzhongshanshuozheqiansuoweiyoudeguangmang。
juewangzaoyibeiyisaoerkong，querdaizhide，shixiongxiongranshaodexiwanghedouzhi！
tazhidao，congjihuozheigexitongkaishi，taderensheng，yijingchedibuyiyangle！
xuezhadenixizhilu，caiganggangkaishi！
ertashouzhongzhei10dianbaoguidexueshenjifen，yijineishenmide“chujishuxuesiwei”suipian，jiushitatashangzheitiaonixizhiludediyitongjin！
jiexialai，gaihaohaoyanjiuyixia，zhei10dianjifen，nengjizijidailaishenmeyangdejingxile！
qinfengdezuijiao，buyouzizhudiyangqiyimochongmanqidaidexiaorong。