在实数范围内分解多项式3x*2+xy-y*2

可以这样算
3x^2 + xy - y^2
等价于
3x^2 + x - 1
分解为(ax - 1)(bx + 1)
得到方程a - b = 1 ab = 3
解出来的a，b是挺难打出来，自己动动手哦
解出来a, b之后代入得到分解后的多项式（ax-y）（ax+y）

3x^2+xy-y^2
=-(y^2-xy)+3x^2
=-(y^2-xy+x^2/4-x^2/4)+3x^2
=-[(y^2-xy+x^2/4)-x^2/4]+3x^2
=-(y-x/2)^2+x^2/4+3x^2
=13x^2/4-(y-x/2)^2
=(√13x/2)^2-(y-x/2)^2
=[√13x/2+(y-x/2)][√13x/2-(y-x/2)]
=[(√13-1)x/2+y][(√13+1)x/2-y].

3x^2+xy-y^2
=3(x^2+2*1/6*xy+1/36*y^2)-1/12*y^2-y^2 {配方}
=3(x+1/6*y)^2-13/12*y^2 {整理}
=3[(x+1/6*y)^2-(√13/6*y)^2] {整理}
=3(x+1/6*y+√13/6*y)(x+1/6*y-√13/6*y) {方差公式}
=3[x+(1+√13)/6*y][x+(1-√13)/6*y] {合并同类项}

3x^2+xy-y^2=(ax+by)^2-(c+1)y^2
=(ax+dy)(ax+ey)
其中
a=3^0.5,b=0.5/a,c=b^2,d=b+c+1,e=b-c-1

(2x^2-y)(x+y)