已知:2x²+3y²-8x+6y+11=0,则x+y=
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x^2+y^2-6x-8y+25=0x^2-6x+9+y^2-8y+16=0(x-3)^2+(y-4)^2=0∴x=3且y=4y/x-x/y=4/3-3/4=7/12
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可以变形为2(X-2)^2+3(y+1)^2=0所以,x=2,y=-1
x^2+y^2-6x-8y+25=0[x-3]^2+[y-4]^2=0x-3=0===>x=3y-4=0===>y=4y/x-x/y=4/3-3/4=7/12
二式乘4得三式,三式减一式得:17X=14得X=14/17将X代入一式,得Y=16/17
5x+2y=6同时乘420x-8y=24用第一个式子加上个式子23x=30x=30/23y代入
根号(x+y-8)+根号(8-x-y)=根号(3x-y-4)+根号(x-2y+7),根据二次根式有意义得:X+Y-8≥0,8-X-Y≥0,∴X+Y≥8,X+Y≤8,∴X+Y=8,左边为0,右边两个非负
x²-6x+8y+y²+25=0x²-6x+9+y²+8y+16=0(x-3)²+(y+4)²=0∴x-3=0y+4=0∴x=3y=-4∴2
可以得出x.x+y.y-6x-8y+25=x.x-6x+9+y.y-8y+16=(x-3).(x-3)+(y-4).(y-4)=0因为(x-3).(x-3)>=0,(y-4).(y-4)>=0所以x=
3x=8yx/y=8/3(1)x+y/y=x/y+1=8/3+1=11/3(2)2x+3y/x-2y分子分母同时除以y得=(2x/y+3)/(x/y-2)=(16/3+3)/(8/3-2)=(25/3
X+Y分之X-Y等于3x=-2yX+Y分之2(x-y)减X+Y分之3X+Y=(-x-3y)/(x+y)=1
解题思路:对于这种等式一定可以化成平方相加的形式,这里面要使用到完全平方公式。解题过程:
因为(x-y)/(x+y)=3,则(x+y)/(x-y)=1/3则5(x-y)(x+y)-(x+y)/2(x-y)=5*3-1/(3*2)=15-1/6=89/6
(x+y)(x-y)-y^2+(x-y)^2-(6x^2y-2xy^2)÷2y=(x+y)(x-y)-y^2+(x-y)^2-2y(3x^2-xy)÷2y=(x+y)(x-y)-y^2+(x-y)^2
x-2y=3则:x=2y+3代入原式,原式=(4y+6+y-6)/(6y+9-y-9)=5y/5y=1
x^2+y^2+8x+6y+25=(x+4)^2+(y+3)^2=0.因为(x+4)^2>=0、(y+3)^2>=0,所以(x+4)^2=0、(y+3)^2=0,即x=-4、y=-3.2x+3y=-8
25拆成9+16(x²-6x+9)+(y²+8y+16)=0(x-3)²+(y+4)²=0平方相加为0则都等于0所以x-3=0,y+4=0x=3,y=-4所以2
(3x+y-6)/(4x-y-8)=[3x+y-3(x-2y)]/[4x-y-4(x-2y)]=5y/7y=5/57
x^2-6x+8y+y^2+25=0x^2-6x+9+y^2+8y+16=0(x-3)^2+(y+4)^2=0(x-3)^2=0,(y+4)^2=0x=3,y=-42x-3y=2*3-3*(-4)=6