x的立方+y的立方+z的立方-3xyz 因式分解, 答案 x^3+y^3+z^3-3xyz =[( x+y)^3-3x^2y-3xy^2]+z^3-3xyz=[(x+y)^3+z^3]-(3x^2y+3xy^2+3xyz)=(x+y+z)[(x+y)^2-(x+y)z+z^2]-3xy(x+y+z) =(x+y+z)(x^2+y^2+2xy-xz-yz+z^2)-3xy(x+y+z) =(x+y+z)(x^...
x^3+y^3+z^3-3xyz =[( x+y)^3-3x^2y-3xy^2]+z^3-3xyz=[(x+y)^3+z^3]-(3x^2y+3xy^2+3xyz)=(x+y+z)[(x+y)^2-(x+y)z+z^2]-3xy(x+y+z) =(x+y+z)(x^2+y^2+2xy-xz-yz+z^2)-3xy(x+y+z) =(x+y+z)(x^2+y^2+z^2-xy-xz-yz) 解析看不懂?免费查看...
首先x, y, z为正整数, x³+y³+z³ > 2012, 在x³, y³, z³中至少有一个 > 2012/3 > 670.x, y, z中至少有一个 > 8, 于是x+y+z > 8.2012 = x³+y³+z³-3xyz = (x+y+z)(x²+y²+z²-xy-yz-...
1.x^2 = 2(y+z) 则x是偶数,设x=2n,得2n^2 = (y+z)2.x^3 = y^3 + z^3 +3xyz得8n^3 = (y+z)^3 - 3yz(y+z) + 3xyz= 8n^6 - 6n^2*yz + 6n*yz=> n!=1 时,yz = 4n^2(n^2+n+1)/3 或者 n=1,x=2,y=z=1 ...
=(x+y-z)[x^2+y^2+z^2+2xy+xz+yz]-3xy(x+y-z) =(x+y-z)[x^2+y^2+z^2-xy+xz+yz] 所以x^3+y^3-z^3+3xyz 能被(x+y-z)整除。 证毕。 用到公式: a^3-b^3=(a+b)(a^2+ab+b^2) (a+b)^3=a^3+b^3+3a^2b+3ab^2反馈...
证明:由于x+y+z=0,故有z=-x-y左边=x^3+y^3+z^3=x^3+y^3+(-x-y)^3=x^3+y^3-(x+y)^3=x^3+y^3-(x^3+3x^2y+3xy^2+y^3)=x^3+y^3-x^3-3x^2y-3xy^2-y^3=-3x^2y-3xy^2右边=3xyz=3xy(-x-y)=-3x^2y-3xy^2所以有:x^3+y^3+z^3=3xyz 解析看不懂?免费查看...
解答一 举报 分别将x=-y-z,y=-x-z,z=-x-y代入X立方+Y立方+Z立方,得到-3y平方z-3z平方y=X立方+Y立方+Z立方,同理可得后两个相加则3(X立方+Y立方+Z立方)=(-3y平方z-3z平方y)+另两个解出来的X+Y+Z=0,即(X+Y+Z)立方=0,展开可得-... 解析看不懂?免费查看同类题视频解析查看解答 ...
解答：由公式：x³＋y³＋z³－3xyz=﹙x＋y＋z﹚﹙x²＋y²＋z²－xy－yz－zx﹚得：x³＋y³＋z³－3xyz=0 ∴x³＋y³＋z³=3xyz。
x+y+z=0 左右两边同时乘X2+y2+z2-xy-xz-yz （X2+y2+z2-xy-xz-yz）乘（x+y+z）=0 打开化简得 x的立方加y的立方加z的立方等于3xyz
x^3+y^3+z^3+2x^2(y+z)+2z^2(x+y)+2y^2(x+z)+3xyz=1 整理得xyz=0 不妨设x=0 又xy+yz+xz=0.5[(x+y+z)^2-(x^2+y^2+z^2)]=-0.5 则y+z=1 y^3+z^3=1 y^4+z^4=(y+z)(y^3+z^3)-yz(y^2+z^2)=4 故x^4+y^4+z^4=4 解析看不懂?免费查看同类题视频解析...