厚膜电阻与薄膜电阻:(x+y)^4+x^4+y^4 提示：换元法

来源：百度文库编辑：高校问答时间：2024/05/04 18:53:22

其中x^n代表x的n次方)
因式分解
不要套公式，谢谢，有巧解

(x + y)^4 + x^4 + y^4
= (x^2 + 2x*y + y^2)^2 + [(x^2 + y^2)^2 - 2x^2*y^2]
= [(x^2 + y^2)^2 + 4xy*(x^2 + y^2) + 4*x^2*y^2] + (x^2 + y^2)^2 - 2x^2*y^2
= 2(x^2 + y^2)^2 + 4xy*(x^2 + y^2) + 2x^2*y^2
= 2[(x^2 + y^2)^2 + 2xy*(x^2 + y^2) + x^2*y^2]
= 2(x^2 + y^2 + xy)^2

先把式子展开得：x^4 + 4x^3*y + 6x^2*y^2 + 4x*y^3 + y^4＋x^4+y^4
然后设x^4=m y^4=n

x + y)^4 + x^4 + y^4
= (x^2 + 2x*y + y^2)^2 + [(x^2 + y^2)^2 - 2x^2*y^2]
= [(x^2 + y^2)^2 + 4xy*(x^2 + y^2) + 4*x^2*y^2] + (x^2 + y^2)^2 - 2x^2*y^2
= 2(x^2 + y^2)^2 + 4xy*(x^2 + y^2) + 2x^2*y^2
= 2[(x^2 + y^2)^2 + 2xy*(x^2 + y^2) + x^2*y^2]
= 2(x^2 + y^2 + xy)^2
先把式子展开得：x^4 + 4x^3*y + 6x^2*y^2 + 4x*y^3 + y^4＋x^4+y^4
然后设x^4=m y^4=n

2X^4+2Y^4+6X^2Y^2+4X^3Y+4XY^3

(x+y)^4+x^4+y^4 提示：换元法 (x+y)^4+x^4+y^4 提示：换元法 (x-y)4*(y-x)3=(y-x)7 () 因式分解(x-y)(x-y)-4(x-y-1) 因式分解:(x+y)(x+y)+4(x-y)(x-y)-4(x·x-y·y) (x-y)^-4(x-y-1) (x+y)2-4(x+y-1) x*x+y*y+4*x-6*y+13=0 x和y等于多少？ 1/4(x+y)+1/2(x+y)*(x+y)>=x*根号y+y*根号x 已知X+Y=-4，求1/2（X+Y)+4(X-Y)-3(X-Y)-3/2(X+Y)-X+Y