已知x+y=9,xy=10,求x^2+y^2,x^3+y^3,x^4+y^4的值.

已知x+y=9,xy=10,求x^2+y^2,x^3+y^3,x^4+y^4的值.
已知x+y=9,xy=10,求x^2+y^2,x^3+y^3,x^4+y^4的值.

已知x+y=9,xy=10,求x^2+y^2,x^3+y^3,x^4+y^4的值.
(x+y)²=81
x²+y²+2xy=81
所以x²+y²=81-2xy=61
x³+y³
=(x+y)(x²-xy+y²)
=9×(61-10)
=459
(x²+y²)²=61²
x^4+2x²y²+y^4=3721
所以x^4+y^4=3721-2(xy)²=3521

(x+y)^2=x^2+y^2+2xy=81
x^2+y^2=81-2xy=61
x^3+y^3=(x+y)(x^2+y^2-xy)=9*(61-10)=459
x^4+y^4=(x^2+y^2)^2-2(xy)^2=61^2-2*100=3521

x+y=9
(x+y)2=x^2+y^2+2xy
x^2+y^2=81-20=61

x+y=9
x²+2xy+y²=81
x²+y²=81-20
=61

1、x²＋y²=(x＋y)²－2xy=9²－20=61
2、x³＋y³=(x＋y)(x²－xy＋y²)=9×(61－10)=459
3、x^4＋y^4=(x²＋y²)²－2(xy)²=61²－200=3521

x^2+y^2=(x+y)^2-2xy=81-20=61;
x^3+y^3=(x^2+y^2)(x+y)-xy(x+y)=61*9-10*9;
x^4+y^4=(x^2+y^2)^2-2x^2y^2=61^2-2*10^2

x²+y²=(x+y)²-2xy=81-20=61
x ³+y³=(x+y)(x²-xy+y²)=9(61-10)=459
x^4+y^4=(x²+y²)²-2x²y²=61²-200=3721-200=3521

x^2+y^2=(x+y)²-2xy=9²-2*10=61
x^3+y^3=(x+y)(x²-xy+y²)
=(x+y)[(x²+y²)-xy]
=9*(61-10)
=459
x^4+y^4
=(x^4+2x²y²+y^4)-2x²y²
=(x²+y²)²-2(xy)²
=61²-2*10²
=3721-200
=3521

这题好多分，围观~

x^2+y^2=(x+y)^2-2xy
x^3+y^3=(x+y)(x^2-xy+y^2)
x^4+y^4=(x^2+y^2)^2-2x^2y^2
将x+y=9,xy=10代入上面式子可得x^2+y^2,x^3+y^3,x^4+y^4为61,459,3521

x^2+y^2=（x+y）^2-2*xy=9*9-2*10=61
x^3+y^3=（x+y)(x^2-xy+y^2)=9*(61-10)=9*51=459
x^4+y^4=(x^2+y^2)^2-2*(x^2y^2)=(x^2+y^2)^2-2*((xy)^2)=61^2-2*(10^2)=3521

x²+y²=(x+y)²-2xy=10²-2*9=100-18=82
x^3+y^3=(x+y)(x²-xy+y²)=(x+y)[(x+y)²-3xy]=9*(9²-3*10)=9*(81-30)=9*49=441
x^4+y^4=x^4+2x²y²+y^4-2x²y²=(x²+y²)²-2x²y²=82²-2*10²=6524
望采纳~谢谢

x^2+y^2=(x+y)^2-2xy=81-20=61;
x^3+y^3=(x+y)^3-3xy(x+y)=729-270=459;
x^4+y^4=(x+y)^4-6(xy)^2-4xy(x^2+y^2)=9^4-600-40*61=3521

解 x^2+y^2=（y+x）^2-2xy=61
x^3+y^3=(x+y)(x^2-xy+y^2)=9*(61-10)=459
x^4+y^4=(x^2+y^2)^2-2x^2y^2=227

x^2+y^2=(x+y)^2-2xy=81-20=61
x^3+y^3=（x+y）*（x^2-xy+y^2）=（x+y）*{（x+y）^2-3xy}=9*（81-30）=459
x^4+y^4=(x^2+y^2)^2-2(xy)^2=61^2-200=3521

很多年前拿手的东西全丢了。如果你是高中的话：
一、先证明X、Y均为整数；
二、举个例子：x^2+y^2=（x+y）^2-2xy，用已知条件可得出结果。后面的同理可得出。祝你好运！