解下列方程组:1)x^2-y^2+x-y=02x^2+4xy-x-6y-3=02)x^2+xy+y^2=38x^2-xy+y^2=143)x^2+xy-2y^2=0x^2+2xy+y^2-x-y-2=04)根号下(x+2)+根号下(y-1)=5x+y=125)m为何值时,方程组x^2-2y^2=6;y=mx-3;有唯一的实数解,并求出这个实数解.6)试
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![解下列方程组:1)x^2-y^2+x-y=02x^2+4xy-x-6y-3=02)x^2+xy+y^2=38x^2-xy+y^2=143)x^2+xy-2y^2=0x^2+2xy+y^2-x-y-2=04)根号下(x+2)+根号下(y-1)=5x+y=125)m为何值时,方程组x^2-2y^2=6;y=mx-3;有唯一的实数解,并求出这个实数解.6)试](/uploads/image/z/1083464-8-4.jpg?t=%E8%A7%A3%E4%B8%8B%E5%88%97%E6%96%B9%E7%A8%8B%E7%BB%84%EF%BC%9A1%29x%5E2-y%5E2%2Bx-y%3D02x%5E2%2B4xy-x-6y-3%3D02%29x%5E2%2Bxy%2By%5E2%3D38x%5E2-xy%2By%5E2%3D143%29x%5E2%2Bxy-2y%5E2%3D0x%5E2%2B2xy%2By%5E2-x-y-2%3D04%29%E6%A0%B9%E5%8F%B7%E4%B8%8B%28x%2B2%29%2B%E6%A0%B9%E5%8F%B7%E4%B8%8B%28y-1%29%3D5x%2By%3D125%29m%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%2C%E6%96%B9%E7%A8%8B%E7%BB%84x%5E2-2y%5E2%3D6%3By%3Dmx-3%3B%E6%9C%89%E5%94%AF%E4%B8%80%E7%9A%84%E5%AE%9E%E6%95%B0%E8%A7%A3%2C%E5%B9%B6%E6%B1%82%E5%87%BA%E8%BF%99%E4%B8%AA%E5%AE%9E%E6%95%B0%E8%A7%A3.6%29%E8%AF%95)
解下列方程组:1)x^2-y^2+x-y=02x^2+4xy-x-6y-3=02)x^2+xy+y^2=38x^2-xy+y^2=143)x^2+xy-2y^2=0x^2+2xy+y^2-x-y-2=04)根号下(x+2)+根号下(y-1)=5x+y=125)m为何值时,方程组x^2-2y^2=6;y=mx-3;有唯一的实数解,并求出这个实数解.6)试
解下列方程组:
1)x^2-y^2+x-y=0
2x^2+4xy-x-6y-3=0
2)x^2+xy+y^2=38
x^2-xy+y^2=14
3)x^2+xy-2y^2=0
x^2+2xy+y^2-x-y-2=0
4)根号下(x+2)+根号下(y-1)=5
x+y=12
5)m为何值时,方程组x^2-2y^2=6;y=mx-3;有唯一的实数解,并求出这个实数解.
6)试讨论方程组x^2+根号下(2y)=a^2+2a+2;根号下(2y)=4x;的实数解的个数.
7)已知方程组x^2+y^2-2x=0;kx-y-k=0;(x,y为未知数)
求证:不论k为何实数,方程组总有两个实数解.
解下列方程组:1)x^2-y^2+x-y=02x^2+4xy-x-6y-3=02)x^2+xy+y^2=38x^2-xy+y^2=143)x^2+xy-2y^2=0x^2+2xy+y^2-x-y-2=04)根号下(x+2)+根号下(y-1)=5x+y=125)m为何值时,方程组x^2-2y^2=6;y=mx-3;有唯一的实数解,并求出这个实数解.6)试
(1)(x,y)=(3/2,-5/2)、(3/2,3/2)、(-1,0)、(-1/3,-1/3)
(2)(x,y)=(3*2^(1/2),2*2^(1/2))、(-3*2^(1/2),2*2^(1/2))、(3*2^(1/2),-2*2^(1/2))、(-3*2^(1/2),-2*2^(1/2))
(3)(x,y)=(-2,1),(4,-2),(-1/2,-1/2),(1,1)
(4)(x,y)=(2,10),(7,5)
(5)将y=mx-3带入x^2-2y^2=6中,得(1-2*m^2)x^2+12mx-24=0,若有唯一解,则二次项系数为0或者判别式为0,得m=(根号2)/2,-(根号2)/2,验证得判别式恒大于0
(6)有根号下(2y)=4x知,x大于等于0,带入第一个方程得x^2+4x-(a^2+2a+2)=0,该方程对称轴为-2,开口向上,令f(x)=x^2+4x-(a^2+2a+2),当x=0时f(0)=-(a^2+2a+2)