(x-y)^2=x+y-1

常见问题解答

• $\text{求解 }x$ ${\left(x-y\right)}^2=x+y-1$

  

  $$\begin{array}{rl}& x=\frac{2y+1+\sqrt{8y-3}}{2}\\ & x=\frac{2y+1-\sqrt{8y-3}}{2}\end{array}$$

• $\text{求解 }y$ ${\left(x-y\right)}^2=x+y-1$

  

  $$\begin{array}{rl}& y=\frac{2x+1+\sqrt{8x-3}}{2}\\ & y=\frac{2x+1-\sqrt{8x-3}}{2}\end{array}$$

• 测试关于原点的对称性 ${\left(x-y\right)}^2=x+y-1$

  

  $$\text{相对于原点不对称}$$

• 测试关于 x 轴的对称性 ${\left(x-y\right)}^2=x+y-1$

  

  $$\text{与x轴不对称}$$

• 测试关于 y 轴的对称性 ${\left(x-y\right)}^2=x+y-1$

  

  $$\text{与y轴不对称}$$

• 以极坐标形式重写 ${\left(x-y\right)}^2=x+y-1$

  

  $$\begin{array}{rl}& r=\frac{\cos \left(\theta \right)+\sin \left(\theta \right)+\sqrt{-3+5\sin \left(2\theta \right)}}{2-2\sin \left(2\theta \right)}\\ & r=\frac{\cos \left(\theta \right)+\sin \left(\theta \right)-\sqrt{-3+5\sin \left(2\theta \right)}}{2-2\sin \left(2\theta \right)}\end{array}$$

• $\text{求关于 }x\text{ 的导数}$ ${\left(x-y\right)}^2=x+y-1$

  

  $$\frac{dy}{dx}=\frac{1-2x+2y}{-2x+2y-1}$$

• $\text{求关于 }y\text{ 的导数}$ ${\left(x-y\right)}^2=x+y-1$

  

  $$\frac{dx}{dy}=\frac{1+2x-2y}{2x-2y-1}$$

• 通过旋转消除 xy 项 ${\left(x-y\right)}^2=x+y-1$

  

  $${\left(y^{\prime }\right)}^2=\frac{\sqrt{2}}{2}\left(x^{\prime }-\frac{1}{\sqrt{2}}\right)$$