z=xy*(a-x-y)求这个数的极值

x²+y²+z²-xy-yz-zx=1/2[(x-y)²+(y-z)²+(z-x)²]=1/2[a²+10²+(a-10

实数x,y,z,满足那么x+y=6,z^2=xy-9,∴xy=z^+9,(x-y)^=(x+y)^-4xy=-4z^>=0,∴z=0,(x+y)^z=6^0=1.

a≠0,xy≠0x≠0且y≠0；同理,b≠0,x≠0,z≠0综上,得x,y,z≠0xy/(x+y)=a(x+y)/(xy)=1/a1/x+1/y=1/a(1)同理1/x+1/z=1/b(2)1/y+1

(太麻烦拉,给点分啊!)设v=x*x-y*y,u=exp{xy}那么dv/dx=2x(这里应该用偏导符号,代替一下),dv/dy=2y,du/dx=y*exp{xy},du/dy=x*exp{xy}那

设(y+z)/x=(z+x)/y=(y+x)/z=k则y+z=kx,z+x=ky,y+x=kz三式相加2(x+y+z)=k(x+y+z)故当x+y+z=0时,k=-1,但xy-z不等于0,可知x+y+

由于x-y=a,z-y=10得x-z=a-10并且由x²+y²+z²-xy-yx-zx=1/2[(x-y)²+(y-z)²+(z-x)²]=

e^y-e^x=xy两边求导,得e^y*y'-e^x=y+xy'(e^y-x)y'=(e^x+y)所以y'=(e^x+y)/(e^y-x)x=0时,e^y-e^0=0,则e^y=1,则y=0所以y'(

首先z'(x)=x*(a-x-2*y)=0z'(y)=y(a-y-2*x)=0计算得到四组解(0,0)(a,0)(0,a)(a/3,a/3)1.(0,0)时,f''xx=0,f''xy=a,f''yy

z=xy+x/y对x的偏导数=y+1/y对y的偏导数=x-x/y^2

x+y=5-z,（x+y）²=（5-z）²,（x+y）²/4＞=xy,（5-z）²/4＞=xyxy+yz+zx=3,xy=3-z（x+y）=3-z（5-z）（5

½(x-y)²+½（x-z）²+½（y-z）²=(4+4a+a²+4-4a+a²+16)÷2=19再问：没有x-z,怎么

令u=xy,v=x+yz=f(u,v)az/ax=y(fu)+(fv)a^2z/axay=a(az/ax)/ay=a(y(fu)+(fv))/ay=(fu)+y(a(fu)/ay)+a(fv)/ay=

设u=xy,v=y/x,则z=f(u,v),所以ðz/ðx=f'1*ðu/ðx+f'2*ðv/ðx=yf'1-yf'2/x^2,注意到f'1

x+y+z=a(x+y+z)^2=a^2(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)x^2+y^2+z^2=(x+y+z)^2-2(xy+yz+zx)=a^2-2

(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)=(x+y)²+2z(x+y)+z²+(x-y)²-z²-2z(x+y)=(x+y)&

确定z=(1+xy)^(x+y)!后面有个阶乘符号吗?阶乘不是连续函数,是不可导的如果忽略阶乘符号z=(1+xy)^(x+y)lnz=(x+y)*ln|1+xy|(∂z/∂x)

(X+Y+Z)^2=x^2+y^2+z^2+2(xy+yz+xz)=a^2=x^2+y^2+z^2+2b所以x^2+y^2+z^2=a^2-2

因为(a+b+c)/3>=开三次方(a*b*c);所以:xy(a-x-y)

因为x+y=8,所以x=8-y所以y（8-y）+z平方+16=0又因为z平方=-16-xy,所以y（8-y）-16-xy=0即8y-y平方-16-xy=0,所以（y-4）平方+xy=0所以z平方=（y