解決{l}{2*cos(x)+5*sec(x)=11}{y=cos(x)}{z=y}{a=z}{text{Solvefor}btext{where}}{b=a} |Microsoft數學求解器

$$\left. \begin{array} { l } { 2 \cdot \cos(x) + 5 \cdot \sec(x) = 11 }\\ { y = \cos(x) }\\ { z = y }\\ { a = z }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

解 x、y、z、a、b (復數求解)

$$x=2\pi n_{1}-i\ln(5-2\sqrt{6})\text{, }n_{1}\in \mathrm{Z}\text{, }y=5\text{, }z=5\text{, }a=5\text{, }b=5$$

$$x=2\pi n_{2}-i\ln(2\sqrt{6}+5)\text{, }n_{2}\in \mathrm{Z}\text{, }y=5\text{, }z=5\text{, }a=5\text{, }b=5$$

$$x=2\pi n_{3}+\frac{5\pi }{3}\text{, }n_{3}\in \mathrm{Z}\text{, }y=\frac{1}{2}=0.5\text{, }z=\frac{1}{2}=0.5\text{, }a=\frac{1}{2}=0.5\text{, }b=\frac{1}{2}=0.5$$

$$x=2\pi n_{4}+\frac{\pi }{3}\text{, }n_{4}\in \mathrm{Z}\text{, }y=\frac{1}{2}=0.5\text{, }z=\frac{1}{2}=0.5\text{, }a=\frac{1}{2}=0.5\text{, }b=\frac{1}{2}=0.5$$

解 x、y、z、a、b

$$x=2\pi n_{1}+\frac{\pi }{3}\text{, }n_{1}\in \mathrm{Z}\text{, }y=\frac{1}{2}=0.5\text{, }z=\frac{1}{2}=0.5\text{, }a=\frac{1}{2}=0.5\text{, }b=\frac{1}{2}=0.5$$

$$x=2\pi n_{2}+\frac{5\pi }{3}\text{, }n_{2}\in \mathrm{Z}\text{, }y=\frac{1}{2}=0.5\text{, }z=\frac{1}{2}=0.5\text{, }a=\frac{1}{2}=0.5\text{, }b=\frac{1}{2}=0.5$$