已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/06 10:58:31
已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值
xO; @!Y9J@ A  BF,B Mrw7ya'.|r7 O ;ƒ3%o&"LYhewۯ$ ߚlEIJOz,jw5UT4p&GAoUq.$y\lg󅘯@,#} E:,7*TFT&-HI[&R=qu"t2\8

已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值
已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值

已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值
x^2y-xy^2-x+y=56
xy(x-y)-(x-y)=56
(xy-1)(x-y)=56
x-y=8
(x-y)^2=8^2
x^2-2xy+y^2=64
x^2+y^2=64+2xy
=64+16
=80

第一步提取x和y,得x（xy）-y（xy）-x+y=56提取xy得xy（x-y）-（x-y）=56得(x-y)(xy-1)=56所以7(x-y)=56，x-y=8，x^2-2xy+y^2=64

已知实数xy满足x+2y 已知实数xy满足 x+y-2 已知xy满足约束条件y=2 2X+y 已知正数x,y满足2x+8y-xy=0,x+y的最小值 已知整数x和y,满足x^+xy-2y^=7,求xy的值 已知实数xy满足x²﹢y²-xy+2x-y+1=0求xy 已知正数xy满足x+2y=2,则x+8y/xy的最小值为? 已知x-xy=8,xy-y=-9,求x+y-2xy的值 已知x.y满足X2-y2=2xy.则x-y/x+y=?x. 已知,xy满足y²=-x²+2x-5/4-y,代数式xy/x+y= 已知正实数x y满足x-根号xy-2y=0求 x+3根号xy+2y/2x-2根号下xy-y 已知正整数x,y满足：xy-x-y=0,则x+2y的最小值 已知实数xy,满足10x²-2xy+y²+6x+1=0,求x+y 已知实数x、y满足xy>0,且8/xy+1/x+1/y=1, 已知xy/x+y=2,求代数式8x-5xy+8y/-x+3xy-y的值 已知实数X,Y满足根号2X-Y-8+根号X+2y+1=0,求XY. 已知正数x y满足x+2y=2 则x+8y/xy 的最小值为 已知正数x,y满足x+8y-xy=0,则x+2y的最小值是