x^3+y^3=(x+y)(x^2-xy+y^2)=(x+y)((x+y)^2-3xy)=4*(16-3)52
x^5+y^5=(x+y)(x^4-x^3y+x^2y^2-xy^3+y^4)
=(x+y)((x^2+y^2)^2-x^2y^2-xy(x^2+y^2))
=4*(14^2-1-14)
=4*181
=724
x^2+y^2=4^2-2=14
x^4+y^4=14^2-2=194
(x^2+y^2)(x^4+y^4)=x^6+x^2y^2(x^2+y^2)+y^6=x^6+y^6+14
14*194=x^6+y^6+14
x^6+y^6=193*14=2702
x^5+y^5=(x+y)(x^5+y^5)=x^6+y^6+xy(x^4+y^4)=2702+194=2896
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已知x+y=4,xy=1,求x^5+y^5
解：x^2+y^2=(x+y)^2-2xy=14 x^3+y^3=(x+y)(x^2-xy+y^2)=(x+y)((x+y)^2-3xy)=4*(16-3)52 x^5+y^5=(x+y)(x^4-x^3y+x^2y^2-xy^3+y^4)=(x+y)((x^2+y^2)^2-x^2y^2-xy(x^2+y^2))=4*(14^2-1-14)=4*181 =724 ...
x+y=3,xy=1,求x^5+y^5
（x³+y³）（x²+y²）=7X18=126=x^5+y^5+x³y²+x²y³=x^5+y^5+x²y²（x+y）=+3 所以x^5+y^5=123
x十y=4,x.y=1求x5次方+y5次方=?
x5+y5=（x+y）（x4+y4-x3.y3）=4{（x2+y2）2-2x2y2-1} =4×193 =772
x+y=4 xy=2 x^5+y^5=? 急!!详细过程
解：x^2+y^2=(x+y)^2-2xy=4^2-2*2=12 x^3+y^3=(x+y)(x^2-xy+y^2)=4*(12-2)=40 所以：x^5+y^5 =(x^2+y^2)*(x^3+y^3)-x^2*y^2*(x+y)=(x^2+y^2)*(x^3+y^3)-(xy)^2*(x+y)=12*40-2^2*4 =480-16 =464 ...
已知x+y=4,xy=1求x五次方y四次方+x四次方y五次方
=(xy)的4次方(x+y)=1的4次方×4 =1×4 =4 (a-b)²-16(a+b)²=[(a-b)+4(a+b)][(a-b)-4(a+b)]=(5a+3b)(-3a-5b)=-(5a+3b)(3a+5b)x³y+xy³+2x²y²=xy(x²+2xy+y²)=xy(x+y)²=4分之3×2²=4...
若x+y=3,xy=1,则x^5+y^5=
x+y=3,xy=1 x²＋y²=（x＋y）²-2xy=9-2=7 x³＋y³=（x＋y）³-3xy（x＋y）=27-9=18 所以 x^5+y^5=（x²＋y²）（x³＋y³）-x²y³-x³y²=（x²＋y²）（x³＋y&#...
已知x+y=4 xy=1,求x2+y2, x3+y3, x4+y4, x5+y5 x6+y6 x7+y7
x2+y2＝(x+y)2-2xy＝14 x3+y3＝(x2+y2)×(x+y)-xy2-yx2＝14×4-xy(x+y)=52 ……剩下的就是这么个算法，手机党，求个最佳哈
x+y=1 x^ +y^ =2,求x^5+y^5
(x+y)²=x²+y²+2xy=1,xy=-1\/2,(x+y)³=x³+y³+3xy(x+y)=1,x³+y³=5\/2,(x²+y²)²=4,x^4 +y^4=7\/2,(x+y)(x^4 +y^4)=x^5+y^5+xy(x³+y³),x^5+y^5-1\/2*5\/2=7\/2,x^5+y^5=19\/4 已赞过 已踩过< 你对这个回答的评价是?
已知x+y=5,xy=3,求x^5+y^5
x+y=5 两边平方 x^2+2xy+y^2=25 x^2+y^2=25-2xy=19 x^3+y^3 =(x+y)(x^2-xy+y^2)=5*(19-3)=80 (x^2+y^2)(x^3+y^3)=x^5+y^5+x^3y^2+x^2y^3 所以x^5+y^5 =(x^2+y^2)(x^3+y^3)-x^2y^2(x+y)=19*80-3^2*5 =1475 ...
解题:已知x+Y=5,xy=3,求x^5+Y^5
x^2+y^2=(x+y)^2-2xy=19 x^3+y^3=(x+y)(x^2-xy+y^2)=5*(19-3)=80 x^5+y^5 =(x^2+y^2)*(x^3+y^3)-x^2*y^2*(x+y)=19*80-9*5 =1520-45 =1475
