第一题x+2/y=y+2/z=√2 求xyz=?

第一题x+2/y=y+2/z=√2 求xyz=?x=√2-2/y (1)y=√2-2/z (2)(2)代入(1)x=√2 -2/(√2-2/z)=√2-2z/(√2z-2)=(2z-2√2-2z)/(√2z-2)=-2√2/(√2z-2) (3)xyz=-2√2/(√2z-2)*(√2-2/z)z=-2√2/(√2z-2)*(√2z-2)=-2√2第二题x+y+z=3 1/x+1/y+1/z=1/3 求(x-3)(y-3)(z-3)=?x³+y³+z³=?x+y+z=3 1/x+1/y+1/z=(yz+xz+xy)/xyz=1/33xy+3yz+3xz=xyz (x-3)(y-3)(z-3)=(xy-3x-3y+9)(z-3)=xyz-3xy-3xz+9x-3yz+9y+9z-27=xyz-(3xy+3yz+3xz)+9(x+y+z)-27=xyz-xyz+9*3-27=0(x+y+z)^2=(x+y+z)(x+y+z)=x^2+xy+xz+xy+y^2+yz+xz+yz+z^2=x^2+y^2+z^2+2xy+2yz+2xz(x+y+z)^3=(x+y+z)^2*(x+y+z)=(x^2+y^2+z^2+2xy+2yz+2xz)(x+y+z)=x^3+yx^2+zx^2+xy^2+y^3+zy^2+xz^2+yz^2+z^3+2yx^2+2xy^2+2xyz+2xyz+2zy^2+2yz^2+2zx^2+2xyz+2xz^2=x^3+y^3+z^3+3xy^2+3yz^2+3xz^2+3yx^2+3zy^2+3zx^2+3xyz+3xyz=x^3+y^3+z^3+3xy(y+x+z)+3yz(z+y+x)+3xz(z+x+y-y)=x^3+y^3+z^3+9xy+9yz+3xz(3-y)=x^3+y^3+z^3+3(3xy+3yz+3xz)-3xyz=x^3+y^3+z^3+3xyz-3xyz=x^3+y^3+z^3x^3+y^3+z^3=(x+y+z)^3=3^3=27