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...
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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...
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