初高中衔接问题 若X+Y+Z=0,则X的三次方+Y的三次方+Z的三次方=? (要过程)
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x^3+y^3+z^3
=x^3+y^3+(-x-y)^3
=x^3+y^3-x^3-y^3-3x^2y-3xy^2
=-3xy(x+y)
=3xyz
成丁嘉立:[答案] 因为x+y+z=0所以x+y=-z x+z=-y(x²-y²-z²)²-4y²z²=[(x+y)(x-y)-z²]²-4y²z²=[-z(x-y)-z²]²-4y²z²=[-z(x-y+z)]²-4y²z²=[-z(-y-...
清新县15769118343: 若x+y+z=0,求x+y+z=3xyz - ?
成丁嘉立:[答案] x+y+z-3xyz=(x+y+z)(x+y+z-xy-yz-xz)
清新县15769118343: x+y+z=0那么x的3次方加y的3次方加z的3次方拜托了各位 也就是这个题咯!若x+y+z=0那么X的3次方加y的3次方加z的3次方等于多少呢?☆★谢谢★☆ - ?
成丁嘉立:[答案] x+y+z=0 则z=-(x+y) z=-(x+y)=-(x+3xy+3xy+y)=-(x+y)-3xy(x+y)=-(x+y)+3xyz x+y+z=3xyz
清新县15769118343: 若x+y+z=0 x三次方+y三次方+z三次方=什么 - ?
成丁嘉立:[答案] x^3+y^3+z^3 =(x+y+z)(x^2+y^2+z^2-xy-yz-zx)+3xyz 故当x+y+z=0时,x^3+y^3+z^3=3xyz
清新县15769118343: 若x+y+z=0,则xyz+(x+y)(y+z)(z+x)=? - ?
成丁嘉立: 因为x+y+z=0 所以x+y=-z y+z=-x z+x=-y 所以xyz+(x+y)(y+z)(z+x)=xyz+(-z)(-x)(-y)=xyz-xyz=0
清新县15769118343: 若x+y+z=0,则x³+y³+z³=? - ?
成丁嘉立: x+y+z=0 则z=-(x+y) z³=-(x+y)³=-(x³+3x²y+3xy²+y³)=-(x³+y³)-3xy(x+y)=-(x³+y³)+3xyz x³+y³+z³=3xyz
清新县15769118343: 已知x+y+z=0,xyz不等于0 - ?
成丁嘉立: 解:由xyz不等于0,x+y+z=0得:x+y=-z;y+z=-x;x+z=-y 即a=x/-x=-1;b=y/-y=-1;c=z/-z=-1 所以原式=-1/-2+-1/-2+-1/-2=3/2
清新县15769118343: 若x+y+z=0,xyz不等于0,求x/丨y+z丨+y/丨x+z丨+z/丨x+y丨的值 - ?
成丁嘉立: 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=8或-1
清新县15769118343: 若x+y+z=0且xyz不等于0,求x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)的值 - ?
成丁嘉立: x+y+z=0 所以x+y=-z x+z=-y y+z=-x x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)=x/y+x/z+y/x+y/z+z/x+z/y=(x+y)/z+(x+z)/y+(y+z)/x=(-z/z)+(-y/y)+(-x/x)=-1-1-1=-3
清新县15769118343: 若x+y+z=0,求x/ |y+z| + y/ |z+x |+z/ |x+y | 的值?
成丁嘉立: x/|y+z| + y/|z+x |+z/|x+y | =x/|x|+y/|y|+z/|z| 首先x,y,z均不为0,否则待求式无意义. 其次x,y,z必定有正有负,否则x+y+z不可能为0 分两种情况: (1)2正1负,x/|x|+y/|y|+z/|z|=1+1-1=1 (2)2负1正,x/|x|+y/|y|+z/|z|=-1-1+1=-1