已知实数x,y满足方程x²+y²-4x-6y=0,则3y-2x的最小值为？ 已知实数x,y满足方程x2+y2-4x+1=0,求： （1）...
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x*2+y*2-4x+1=0\u5373\uff08x-2\uff09*2+y*2=3
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\u4f5c\u56fe\u53ef\u5f97\u6700\u5927\u503c\u4e3a\u6839\u53f73,\u6700\u5c0f\u503c\u4e3a-\u6839\u53f73
\u540c\u7406X^2+Y^2\u8868\u793a\u4ee5\u539f\u70b9\u4e3a\u5706\u5fc3\u7684\u56ed\u7684\u534a\u5f84\u7684\u5e73\u65b9
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\u65b9\u7a0bx2+y2-4x+1=0\u662f\u7ea6\u675f\u6761\u4ef6\uff0c\u51e0\u4f55\u4e0a\u5b83\u8868\u793a\u5e73\u9762\u4e0a\u4e2d\u5fc3\u5728\u70b9\uff082,0\uff09\u534a\u5f84\u4e3a\u6839\u53f73\u7684\u5706\u3002
\uff081\uff09\u7528y/x=k\uff0c\u5373\u8fc7\u539f\u70b9\u7684\u76f4\u7ebfy=kx\u548c\u4e0a\u8ff0\u5706\u76f8\u5207\uff0c\uff08\u67092\u6761\u5207\u7ebf\uff09\u5bf9\u5e94\u7684k\u4fbf\u662f\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\uff1b
\uff082\uff09\u7528x^2+y^2=r\uff0c\u5373\u5706x^2+y^2=r\u548c\u4e0a\u8ff0\u5706\u76f8\u5207\uff0c\uff08\u67092\u4e2a\u5207\u5706\uff09\u5bf9\u5e94\u7684r\u4fbf\u662f\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\uff1b
\uff083\uff09\u7528y-x=c\uff0c\u5373\u659c\u7387\u4e3a1\u7684\u76f4\u7ebfy=x+c\u548c\u4e0a\u8ff0\u5706\u76f8\u5207\uff0c\uff08\u67092\u6761\u5207\u7ebf\uff09\u5bf9\u5e94\u7684c\u4fbf\u662f\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c.
最小化|函数|3 y-2 x
定义域|-4 x+x ^2-6 y+y ^2=0
min{3 y - 2 x|x^2 - 4 x + y^2 - 6 y = 0} = -8 at (x, y) = (4, 0)
绛旓細x^2+y^2-4x+1=0 鍖栦负(x-2)^2+y^2=3锛屾槸鍦嗗績鍦(2,0)鍗婂緞涓烘牴鍙(3)鐨勫渾 y/x鐞嗚В涓哄渾涓婁竴鐐逛笌鍘熺偣杩炵嚎鏂滅巼锛屽鍥 鍗充负鏈澶у拰鏈灏忕殑鎯呭喌 鍦ㄧ敱濡傚浘鐩磋涓夎褰㈠叧绯诲彲鐭ユ渶澶т负 鏍瑰彿(3)锛屾渶灏 -鏍瑰彿(3)
绛旓細y = -sqrt (x^2 - 1) (x 鈮 1)3. x < 0涓攜 鈮 0:-x^2 + y^2 = 1 y^2 = x^2 + 1 y = 卤sqrt (x^2 + 1)鍥犲凡璁緔 鈮 0,y = sqrt (x^2 + 1) (x < 0)4. x < 0 涓 y < 0:-x^2 - y^2 = 1 x,y 涓瀹炴暟鏃朵笉鍙兘.缁撳悎1-3:f(x) =...
绛旓細(1)璁緔/(x-4)锛漷鈫抰x-y-4t锛0.姝ょ洿绾跨郴涓庡渾鐩镐氦鍒欎笌鍦嗗績(-1,2)鐨勮窛绂讳笉澶т簬鍗婂緞2,鈭磡t路(-1)-2-4t|/鈭(t²+1)鈮2 鈫21t²+20t鈮0 鈫-20/21鈮鈮0.鏁呮墍姹傛渶澶у间负0,鎵姹傛渶灏忓间负-20/21.(2)璁2x-y锛漸鈫2x-y-u锛0.姝ょ洿绾跨郴涓庡渾蹇(-1,2)璺濈涓嶅ぇ浜...
绛旓細宸茬煡瀹炴暟X,Y婊¤冻鏂圭▼X骞虫柟+Y骞虫柟鈥4X+1=0 锛1锛夋眰Y鈥擷鐨勬渶澶у煎拰鏈灏忓.锛2锛夋眰X骞虫柟+Y骞虫柟鐨勬渶澶у煎拰鏈灏忓.锛1锛夊師鏂圭▼鍙寲涓猴細(x-2)^2+y^2=3,鏄渾蹇冧负(2,0),鍗婂緞涓衡垰3鐨勫渾鐨勮建杩规柟绋.璁緔-x=z1,閭1灏辨槸鐩寸嚎y-x=z1鐨勭旱鎴窛.鍥犳褰撳浜庡浘1涓瑼C鐨勪綅缃椂,y-x=z1鐨...
绛旓細鍘鏂圭▼鍙寲涓猴細(x-2)²+y²=3 杩欐槸鍦嗗績鍦紙2,0锛夊崐寰勭瓑浜庘垰3鐨勫渾锛婊¤冻璇ユ柟绋嬬殑鐐筆(x,y)鍦ㄥ渾涓,骞朵笖y/x涓虹洿绾縊P鐨勬枩鐜囥傛樉鐒讹紝褰揙P涓庡渾鐩稿垏锛屽苟涓斾綅浜庣涓璞￠檺鏃讹紝鍏舵枩鐜囨渶澶с備护OP鐨勬柟绋嬩负 y=kx锛屼唬鍏ュ師鏂圭▼寰 (1+k²)x²-4x+1=0 浠ゅ垽鍒紡 鈻=16-4(1+...
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绛旓細璁 x^2+y^2=t 锛屼唬鍏ュ彲寰 t+4x+1=0 锛屾柟绋閰嶆柟鍙緱 (x+2)^2+y^2=3 锛屾墍浠ワ紝鍦 (x+2)^2+y^2=3 涓庣洿绾 t+4x+1=0 鏈夊叕鍏辩偣 锛屽垯鍦嗗績鍒扮洿绾跨殑璺濈涓嶈秴杩囧渾鐨勫崐寰勶紝鍗 |t-8+1|/4<=鈭3 锛岃В寰 7-4鈭3<=t<=7+4鈭3 锛屼篃灏辨槸璇锛寈^2+y^2 鐨勬渶澶у间负 7+4鈭3 ...
绛旓細锛堬紞鈭烇紝锛1.5]鈭猍0.5锛+鈭烇級
绛旓細(1)璁(y+2)/(x+1)=k锛寉+2=k(x+1)锛屽彲鐪嬪仛鍦嗕笂鐨勭偣鍒扮偣(-1,-2)鐨勬枩鐜囷紝姹傚嚭杩(-1,-2)鐨勪袱鏉″垏绾鏂圭▼锛屼袱涓枩鐜囧嵆涓烘渶鍊 (2)璁緓-2y=p锛寉=x/2-p/2锛寈-2y涓烘渶灏忓煎嵆p涓烘渶灏忓兼椂锛岋紙-p/2锛変负鏈澶у硷紝杩囧師鐐瑰仛涓鏉℃枩鐜囦负1/2鐨勭洿绾匡紝鍚戜笂骞崇Щ锛岀洿鑷充笌鍦嗙浉鍒(杩欓兘鏄...
