因式分解
因式分解 已知X+Y=4 X^2+Y^2=14 求X^5方+Y^5方 的值
参考答案:x+y=4, x^2+y^2=14 ===> xy=1
x^3+y^3=(x+y)(x^2+y^2-xy)
=4*(14-1)
=52
(x^2+y^2)(x^3+y^3)=x^5+y^5+(xy)^2*(x+y)
x^5+y^5=(x^2+y^2)(x^3+y^3)-(xy)^2*(x+y)
=14*52-1*4
=728-4
=724
因式分解 已知X+Y=4 X^2+Y^2=14 求X^5方+Y^5方 的值
参考答案:x+y=4, x^2+y^2=14 ===> xy=1
x^3+y^3=(x+y)(x^2+y^2-xy)
=4*(14-1)
=52
(x^2+y^2)(x^3+y^3)=x^5+y^5+(xy)^2*(x+y)
x^5+y^5=(x^2+y^2)(x^3+y^3)-(xy)^2*(x+y)
=14*52-1*4
=728-4
=724