已知x平方加y平方-6x 8y=-25,求x.y-搜答案-智慧作业帮

把25拆成16+9(x²-8x+16)+(y²+6y+9)=0(x-4)²+(y+3)²=0平方大于等于0,相加等于0若有一个大于0,则另一个小于0,不成立.所

x^2+2x+y^2-6y+10=0=(x^2+2x+1)+(y^2-6y+9)=0=(x+1)^2+(y^2-6y+3^2)=0=(x+1)^2+(y-3)^2=0x=-1y=3xy=-3

即(x²+4x+4)+(y²-6y+9)=0(x+2)²+(y-3)²=0所以x+2=0,y-3=0x=-2,y=3所以x-y=-5

x+y=5(x+y)²=25x²+2xy+y²=25x²+y²=25-2xyx²+y²=25-12x²+y²=

N－M=4xy

x^2-2x+y^2+6y+10=0x^2-2x+1+y^2+6y+9=0(x-1)^2+(y+3)^2=0x-1=0,y+3=0x=1,y=-3(x-y)/(x+y)=4/(-2)=-2

x^2+y^2=6y-4x-13x^2+4x+4+y^2-6y+9=0(x+2)^2+(y-3)^2=0x=-2y=3x^2-y^2=(-2)^2-3^2=4-9=-5

（x-y)²=x²+y²-2xy=x²+y²+2xy-4xy=(x+y)²-4xy=7²-2[(x+y)²-x²

x平方加y平方减2xy减6x加6y加9=0x^2+y^2-2xy-6x+6y+9=0(x^2+y^2-2xy)-6(x-y)+9=0(x-y)^2-6(x-y)+9=0(x-y-3)^2=0x-y-3

把10拆成1+9(x²+2x+1)+(y²+6y+9)=0(x-1)²+(y+3)²=0平方大于等于0,相加等于0若有一个大于0,则另一个小于0,不成立.所以两

x²+2x+1+y²-6y+9=0(x+1)²+(y-3)²=0∴x+1=0y-3=0∴x=-1y=3

x^2+y^2-6x+4y+13=0x^2-6x+9+y^2+4y+4=0(x-3)^2+(y+2)^2=0又因为(x-3)^2>=0;(y+2)^2>=0;所以(x-3)^2=0,(y+2)^2=0

(x平方+y平方)平方-y平方=x平方+6所以（x²＋y²）²-（x²＋y²）-6=0（x²＋y²＋2）（x²＋y

x²-2x+y²+6y+10=0(x²-2x+1)+(y²+6y+9)=0(x-1)²+(y+3)²=0∴x-1=0,y+3=0∴x=1,y

x=-4y=-3=-516

由x+y=25x+y=7则(x+y)=x+y+2xy=7=492xy=(x+y)-（x+y）=49-25=24则（x-y)=x+y-2xy=25-24=1因为：x＜y所以x-y＜0即x-y=-1

x的平方加y的平方加2x-6y+10=0即：(x+1)^2+(y-3)^2=0所以：x=-1,y=3.所以：x+y=2.

原方程化为（x+1）^2-(y-3)^2=0化简得|x+1|=|y-3|由于x+y≠2,所以x+1=y-3故x-y=-4

由题意可得x²+y²+2x+6y+10=0（x+1）²+（y+3）²=0所以x=-1,y=-3