这道题用拉格朗日乘数法怎么做？. 请用拉格朗日乘数法解这道题
\u6c42\u4f60\u4eec\u4e00\u9053\u9898\uff01\u7528\u62c9\u683c\u6717\u65e5\u4e58\u6570\u6cd5\u505a\uff01g(x)=x^2+y^2-3 +k(x-y+1)
dg/dx = 2x +k =0
dg/dy = 2y-k =0
dg/dk = x-y+1=0
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-k/2 -k/2 +1 =0, k=1, x=-0.5, y=0.5
\u6781\u503c\u4e3a0.5^2+0.5^2 -3 =-2.5
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V=xyzx^2+y^2+z^2=4a^2F(x,y,z)=xyz+λ(x^2+y^2+z^2-4a^2)所有F方程的偏微分设为零,得到一个方程组:yz+2λx=0xz+2λy=0xy+2λz=0而:x^2+y^2+z^2=4a^2解方程组,得:x=y=z=(2/3)(根号3)a最大体积=xyz=(8/9)(根号3)a^3绛旓細濡傚浘鎵绀猴細
绛旓細g(x)=x^2+y^2-3 +k(x-y+1)dg/dx = 2x +k =0 dg/dy = 2y-k =0 dg/dk = x-y+1=0 杩欐槸涓涓笁鍏冧竴娆℃柟绋嬬粍锛屽緢瀹规槗寰楀埌 -k/2 -k/2 +1 =0, k=1, x=-0.5, y=0.5 鏋佸间负0.5^2+0.5^2 -3 =-2.5 ...
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绛旓細瀵逛簬鍑芥暟 z = x^2 + y^2 鍦ㄦ潯浠 (x/a) + (y/b) = 1 涓嬫眰鏋佸硷紝鍙互浣跨敤鎷夋牸鏈楁棩涔樻暟娉銆傞鍏堬紝鎴戜滑瀹氫箟鎷夋牸鏈楁棩鍑芥暟 L(x, y, 位) = x^2 + y^2 + 位((x/a) + (y/b) - 1)銆傚叾涓紝位涓烘媺鏍兼湕鏃ヤ箻瀛愩傛眰瑙ｆ瀬鍊肩殑姝ラ濡備笅锛1. 璁＄畻 L 瀵 x 鐨勫亸瀵兼暟锛屽苟浠ゅ叾绛変簬闆讹細&#...
绛旓細鍋囪闀挎柟浣撶殑闀夸负x锛屽涓簓锛岄珮涓簔锛岄偅涔堣〃闈㈢Н涓6銆傛牴鎹暱鏂逛綋琛ㄩ潰绉叕寮忥紝鎴戜滑鍙互鍐欏嚭锛2(xy + xz + yz) = 6 瑕佷娇闀挎柟浣撶殑浣撶НV = xyz鏈澶э紝鎴戜滑闇瑕浣跨敤鎷夋牸鏈楁棩涔樻暟娉鏉ヨВ鍐宠繖涓害鏉熶紭鍖栭棶棰樸傛垜浠彲浠ュ皢涓婅堪鍏紡鍖栫畝涓猴細xy + xz + yz = 3 瀹氫箟鎷夋牸鏈楁棩鍑芥暟锛歀(x, y, z, 位) =...
绛旓細璁鹃暱瀹介珮鍒嗗埆涓簒,y,z 琛ㄩ潰绉紳xy+2xz+2yz=a V=xyz 鎵浠ュ彧闇瑕佹眰V鍦▁y+2xz+2yz锛峚=0鏉′欢涓嬬殑鏈鍊 浠(位锛=xyz+(xy+2xz+2yz-a)位 Fx=yz+(y+2z)位=0鈶 Fy=xz+(x+2z)位=0鈶 Fz=xy+(2x+2y)位=0鈶 F位=xy+2xz+2yz-a=0鈶 鈶犆梮: xyz+x(y+2z)位=0 鈶∶梱: xyz...
绛旓細璁炬按绠辩殑闀裤佸銆侀珮鍒嗗埆涓 x锛寉锛寊锛屽垯姘寸瀹圭НV=xyz锛岀剨鍒舵按绠辩敤鍘荤殑閽㈡澘闈㈢Н涓篠=2(xz+yz)+xy锛岃繖瀹為檯涓婃槸姹傚嚱鏁癝(x锛寉锛寊)鍦ㄦ潯浠秞yz-V=0闄愬埗涓嬬殑鏈灏忓奸棶棰樸傚簲鐢鎷夋牸鏈楁棩涔樻硶锛屼护 L='2*(x*z+y*z)+x*y+v*(x*y*z-V)'锛沝Ldx=diff(L,'x')锛宒Ldy=diff(L,'y')锛宒Ldz...
绛旓細鐢ㄢ鎷夋牸鏈楁棩涔樻暟娉鈥濇眰鏋佸 姹傚嚱鏁癴(x,y,z)鍦ㄦ潯浠断(x,y,z)=0涓嬬殑鏋佸 鏂规硶锛堟楠わ級鏄細1銆鍋氭媺鏍兼湕鏃鍑芥暟L=f(x,y,z)+位蠁(x,y,z),位绉版媺鏍兼湕鏃ヤ箻鏁 2銆傛眰L鍒嗗埆瀵箈,y,z,位姹傚亸瀵,寰楁柟绋嬬粍,姹傚嚭椹荤偣P(x,y,z)濡傛灉杩欎釜瀹為檯闂鐨勬渶澶ф垨鏈灏忓煎瓨鍦,涓鑸鏉ラ┗鐐瑰敮涓,浜庢槸鏈鍊 ...
