求曲线x² y²-z²=0,z=x 1,在XOY面上的投影曲线方程
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(x+y-z)/z=(y+z-x)/x=(z+x-y)/y[x+y]/z-1=[y+z]/x-1=[z+x]/y-1[x+y]/z=[y+z]/x=[z+x]/y设[x+y]/z=[y+z]/x=[z
设(y+z)/x=(x+z)/y=(x+y)/z=k;y+z=kx;x+z=ky;y+z=kx;2(x+y+z)=k(x+y+z);k=2或x+y+z=0;所以,(y+z)(x+z)(x+y)/xyz
x/(y+z)=y/(x+z)=z/(x+y)当x+y+z=0时,x+y=-z(x+y)/z=-z/z=-1当x+y+z≠0时,由x/(y+z)=y/(x+z)=z/(x+y)根据等比性质可得(x+y
x+y-z=6y+z-x=2z+x-y=0三式相加得x+y+z=8-得2z=2z=1-得2x=6x=3-得2y=8y=4x=3y=4z=1
设(x+y-z)/z=(x-y+z)/y=(-x+y+z)/x=k则(1)x+y-z=kz(2)x-y+z=ky(3)-x+y+z=kx(1)+(2)+(3)得x+y+z=k(x+y+z)∴k=1时,
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+
令(y+z)/x=(z+x)/y=(x+y)/z=t∴y+z=xt,z+x=yt,x+y=zt三式相加得:2(x+y+z)=(x+y+z)t∴(2-t)(x+y+z)=0∴2-t=0或x+y+z=0若
∵y+z÷x=Z+X÷y=X+Y÷z容易发现x,y,z位置互换也成立∴式子与x,y,z值无关∴x=y=z∴(X+Y-Z)÷(X+Y+z)=x/3x=1/3明教为您解答,请点击[满意答案];如若您有不满
x+y+z-6=02x+3y-z-12=02x-y-z=0组成方程组再解x=2y=3z=1
两端对x求偏导得:-ye^(-xy)-2(z/x)+(z/x)e^z=0,所以,z/x=ye^(-xy)/(e^z-2)两端对y求偏导得:-xe^(-xy)-2(z/y)+(z/y)e^z=0,所以,
设:(x+y-z)/z=(y+z-x)/x=(z+x-y)/y=k{x+y-z=kz(1){y+z-x=kx(2){z+x-y=ky(3)(1)+(2)+(3)得:(x+y+z)=k(x+y+z)(x
两式相减,得3x-4z=0x=4/3zx:z=4:3代入,得y=7/9zy:z=7:9
4x-3y-3z=0.1)x-3y+z=0.2)相减:3x=4zx/z=4/31)-2)*4:9y=7zy/z=7/9所以:x/z=4/3,y/z=7/9
令(y+z)/x=(z+x)/y=(x+y)/z=ky+z=kxx+z=kyx+y=kz2(x+y+z)=k(x+y+z)2(x+y+z)=k(x+y+z)(2-k)(x+y+z)=0(x+y+z≠0
4x-3y-3z=0(1)x-3y+z=0(2)(1)-(2):3x-4z=0x=4z/3代入(1):16z/3-3y-3z=0y=7z/9所以:x:z=4:3y:z=7:9
1.z²-z+1/4=(z-1/2)².绝对值、根号、平方数都是非负的,而相加为0.所以都为0.即x=y,2y=z,z=1/2.所以x=y=1/4,z=1/2.2.2002x200
设x+y-z/z=x-y+z/y=y+z-x/x=k有x+y-z=kzx-y+z=kyy+z-x=kx三式相加得x+y+z=k(x+y+z)k=1得x+y=(k+1)zx+z=(k+1)yy+z=(k
4x-3y-3z=0①x-3y+z=0②①-②,得3x-4z=03x=4z由于z不等于0,故有x:z=4:3同理可得:①-4②,得9y-7z=09y=7zy:z=7:9
两式相加,得6X-5Z=0即X=5Z/6,即X/Z=5/6.再将X=5Z/6代入式1,得5Y+11Z/2=0得Y/Z=-11/10
括号是什么意思?只有一半