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已知x+y=2.xy=½.求1.½x²+½y&#...

解: x²+y²+xy=3 x²+xy+¼y²+¾y²=3 (x+½y)²+[(√3/2)y]²=3 令x+½y=√3cosα,(√3/2)y=√3sinα 则x=√3cosα-sinα,y=2sinα x²+y² =(√3cosα-sinα)²+(2sinα)² =3cos²α+...

求微分方程 x²dy=(y²-xy+x²)dx的通解 解:两边同除以x²得:dy=[(y/x)²-(y/x)+1]dx,即y'=(y/x)²-(y/x)+1........① 令y/x=u,则y=ux.........②;故y'=u+xu';代入①式得:u+xu'=u²-u+1; 化简得:xu'=u²-2...

z=f(x²+y²,e^(xy)),求z对x,y的二阶偏导数 解:设z=f(u,v);u=x²+y²;v=e^(xy);则: ∂z/∂x=(∂f/∂u)(∂u/∂x)+(∂f/∂v)(∂v/∂x) =2x(∂f/∂u)+ye^(xy)...

1、最简单也是最笨的方法就是直接解x/y/z 由题:x+y=2-z (x+y)²=(2-z)² x²+y²=14-z² 化简得:2z^3-4z^2-10z+12=0 观察这个式子,很简单的看出来z可以等于1,但是三次方程有三个解,其他两个解待定。 观察已知的三个...

e^xy+x²·y=1,两边对x求导 e^xy·(y+xy')+2xy+x²y'=0 y'(xe^xy+x²)=-ye^xy-2xy y'=-(ye^xy+2xy)/(xe^xy+x²)

x+y=(1+1)/2=1 x-y=(2√3-2√2)/2=√3+√2 所以x²-y²=(x+y)(x-y)=√3+√2 xy=[[1-(√2-√3)²]/4 =(1-5+2√6)/4 =(√6-2)/2 原式=(√3+√2)²/4+(√6-2)/2 =(5+2√6)/4+(√6-2)/2 =(4√6+1)/4

x³-x²y-xy²+y³ =(x³+y³)-(x²y+xy²) =(x+y)(x²-xy+y²)-xy(x+y) =(x+y)(x²-xy+y²-xy) =(x+y)(x²-2xy+y²) =(x+y)(x-y)²

我想原题是这样“已知x(x + 1) -(x² + y ) = 3, 求 x - y =?”这样的吧。如果是的话。可以这样来解答: 解:∵x(x + 1) -(x² + y ) = 3 x² + x -(x² + y )= 3 x² + x - x² - y = 3 ∴ x - ...

d²y/dx² =d(dy/dx)/dx =[(1-y')(x+y)-(1+y')(x-y)]/(x-y)² =(x+y-xy'-y'y-x+y-xy'+y'y)/(x-y)² =(2y-xy')/(x-y)² =[2y-x(x+y)/(x-y)]/(x-y)² =[2y(x-y)-x(x+y)]/(x-y)³ =(2xy-2y²-x²-xy)/(x-y)...

x²-3xy+2y² = (x-y)(x-2y) x²-3xy+y² = (x-3/2y)²-5/4y² = { x-(3+√5)/2y } { x-(3-√5)/2y }

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