1楼
x^7+y^14=x^7+(y^2)^7=
=(x+y^2)[(x^6)-(x^5)y^2+(x^4)(y^2)^2-x^3(y^2)^3+x^2(y^2)^4-x(y^2)^5+(y^2)^6]=(x+y^2)[(x^6)-(x^5)y^2+(x^4)y^4-x^3y^6+x^2y^8-xy^10+y^12]
=(x+y^2)[(x^6)-(x^5)y^2+(x^4)(y^2)^2-x^3(y^2)^3+x^2(y^2)^4-x(y^2)^5+(y^2)^6]=(x+y^2)[(x^6)-(x^5)y^2+(x^4)y^4-x^3y^6+x^2y^8-xy^10+y^12]
2楼
如果你学了复数,就好分解多了.
令x^7+y^14=0
得解为x=-y^2(cos(2nπ/7)+isin(2nπ/7))(n=0.1.2.3.4.5.6)
x+y^2(cos(2nπ/7)+isin(2nπ/7))就是它的7个因式(n=0 1 2 3 4 5 6 7)
令x^7+y^14=0
得解为x=-y^2(cos(2nπ/7)+isin(2nπ/7))(n=0.1.2.3.4.5.6)
x+y^2(cos(2nπ/7)+isin(2nπ/7))就是它的7个因式(n=0 1 2 3 4 5 6 7)
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