解決a^{2}c^{2}-b^2c^2=a^4-b^4.i |Microsoft數學求解器

$$a ^ { 2 } c ^ { 2 } - b ^ { 2 } c ^ { 2 } = a ^ { 4 } - b ^ { 4 } . i$$

解 a (復數求解)

$$a=\sqrt{c^{2}-b^{2}}$$

$$a=-\sqrt{c^{2}-b^{2}}$$

$$a=-b$$

$$a=b$$

解 b (復數求解)

$$b=a$$

$$b=-a$$

$$b=-\sqrt{c^{2}-a^{2}}$$

$$b=\sqrt{c^{2}-a^{2}}$$

解 a

$$\left\{\begin{matrix}\\a=-b\text{; }a=b\text{, }&\text{unconditionally}\\a=-\sqrt{c^{2}-b^{2}}\text{; }a=\sqrt{c^{2}-b^{2}}\text{, }&|c|\geq |b|\end{matrix}\right.$$

解 b

$$\left\{\begin{matrix}\\b=-a\text{; }b=a\text{, }&\text{unconditionally}\\b=-\sqrt{c^{2}-a^{2}}\text{; }b=\sqrt{c^{2}-a^{2}}\text{, }&|a|\leq |c|\end{matrix}\right.$$