X+Y=10,X^3+Y^3=400,求X^2+Y^2

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 21:05:43

X+Y=10,X^3+Y^3=400,求X^2+Y^2
X+Y=10,X^3+Y^3=400,求X^2+Y^2

X+Y=10,X^3+Y^3=400,求X^2+Y^2
(x+y)^3=x^3+3x^2 y+3xy^2+y^3=x^3+y^3+3xy(x+y)=400+3xy*10=1000
xy=20
(x+y)^2=x^2+y^2+2xy=100
x^2+y^2=60

x+y=10
x^2+y^2+2xy=100
x^2+y^2=100-2xy
x^3+y^3=(x+y)(x^2+y^2-xy)=400
则
10*(100-2xy-xy)=400
xy=20
则x^2+y^2=100-2*20=60

xy=50吧

400=x^3+y^3=(x+y)(x^2+y^2+xy)=(x+y)((x+y)^2-xy)=100(100-xy)
so xy=96
x^2+y^2=(x+y)^2-2xy=100-2*96=-92

因为
(x+y)^3=x^3+y^3+3xy(x+y)=10^3=1000
所以xy=20
之后有2种方法
1.x^3+y^3=(x+y)(x^2-xy+y^2)=400
所以x^2-xy+y^2=40 所以x^2+y^2=60
2.(x+y)^2=x^2+y^2+2xy=100
所以x^2+y^2=60

(x+y)(x+y-10)+25=0,且x-y=3,求x,y (x+y)(x+y-10)+25=0,且x-y=3,求x,y 已知:3x-5y=0,求x/y,x-y/y,x-y/x X+Y=10,X^3+Y^3=400,求X^2+Y^2 已知x+y=10,x^3+y^3=400,求x^2+y^2 已知x-y/x+y=3,求代数式5(x-y)/x+y-x+y/2(x-y) 已知3x =2y 求x/x+y+y/x-y-y²/x²-y² 已知x-y=3,求[（x+y)(x-y)-(x-y)^2+2y(x-y)]除以的值已知|x|=2,|y|=3,|x+y|=-(x+y)求x-y (x-y)/(x+y)=3求( 3x-2y-1)/(x+y-5) x(x-3y)=4y(x-3y),求x:y y=3(x-y),x=2(x-y)求x,y的值已知|3x-y|+|x+y|=0,求x-y除以x*y的值. 若2/x-1/y=3,求[y/x-y/x-y(x-y/x-x+y)]/x-2y/x的值 y=x^3-cosx,求y x+y=2,3x+7y=10 求x和y (x+y-5)+|3y-2x+10|=0,求 x,y的值已知x-y=3 ,(x+y）（x+y+10)+25=0 求x,y的值