已知实数x、y满足x+y+xy=9,x2y+xy2=20,求x2+y2的值.
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/05/14 04:53:09
已知实数x、y满足x+y+xy=9,x2y+xy2=20,求x2+y2的值.
2是平方的意思.
2是平方的意思.
x+y+xy=9
x+y=9-xy
x^2y+xy^2=20
xy(x+y)=20
xy(9-xy)=20
xy^2-9xy+20=0
(xy-4)(xy-5)=0
xy=4或xy=5
x+y=5或x+y=4
x^2+y^2
=(x+y)^2-2xy
=4^2-2*5
=6
或
x^2+y^2
=(x+y)^2-2xy
=5^2-2*4
=17
所以x^2+y^2的值为6或17
x+y=9-xy
x^2y+xy^2=20
xy(x+y)=20
xy(9-xy)=20
xy^2-9xy+20=0
(xy-4)(xy-5)=0
xy=4或xy=5
x+y=5或x+y=4
x^2+y^2
=(x+y)^2-2xy
=4^2-2*5
=6
或
x^2+y^2
=(x+y)^2-2xy
=5^2-2*4
=17
所以x^2+y^2的值为6或17
已知实数x、y满足x+y+xy=9,x2y+xy2=20,求x2+y2的值.
已知x、y均为实数,且满足xy+x+y=17,x2y+xy2=66,求x2+y2
已知x.y是正整数,并且xy+x+y=23,x2y+xy2=120.求x2+y2的值
已知x和y是正整数,并且满足条件xy+x+y=71,x2y+xy2=880,求x2+y2的值.
已知x+y=3,xy=1,求代数式①x2y+xy2;②x2+y2的值.
已知(x+3)2+▕x-y+10▏=0求代数式5x2y-【2x2-(3xy-xy2)-3x2】-2xy2-y2的值.
已知X2+4y2-4x+4y+5=0 求x-y的值 已知xy=4满足x2y-xy2-x+y=56,求x2+y2的值
已知x-y≠0 x2-x=7 y2-y=7 求x3+y3+x2y+xy2的值
已知x、y均为实数,且满足xy+x+y=17,x2y+xy2=66,求x4+x3y+x2y2+xy3+y4的值.
已知x+y=-5,xy=7,求x2y+xy2-x-y的值.
已知实数x,y满足(x2)+(y2)-xy+2x-y+1=0,求x,y的值
已知实数x、y满足X2+y2-xy+2x-y+1=0,试求x、y的值