{l}{4x^2-5x-1=0}{y=7+10beta-8beta^2}{z=y}{a=z}{b=a}{c=b}{text{Solvefor}dtext{where}}{d=c} حل کریں

$$\left. \begin{array} { l } { 4 x ^ {2} - 5 x - 1 = 0 }\\ { y = 7 + 10 \beta - 8 \beta ^ {2} }\\ { z = y }\\ { a = z }\\ { b = a }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

x، y، z کے لئے حل کریں (complex solution)

$$x=\frac{5-\sqrt{41}}{8}\approx -0.17539053\text{, }y=7+10\beta -8\beta ^{2}\text{, }z=7+10\beta -8\beta ^{2}$$

$$x=\frac{\sqrt{41}+5}{8}\approx 1.42539053\text{, }y=7+10\beta -8\beta ^{2}\text{, }z=7+10\beta -8\beta ^{2}\text{, }\left(\beta =\frac{-\sqrt{81-8d}+5}{8}\text{ or }\beta =\frac{\sqrt{81-8d}+5}{8}\right)\text{ and }a=d\text{ and }c=d\text{ and }b=d$$

x، y، z کے لئے حل کریں

$$x=\frac{5-\sqrt{41}}{8}\text{, }y=7+10\beta -8\beta ^{2}\text{, }z=7+10\beta -8\beta ^{2}$$

$$x=\frac{\sqrt{41}+5}{8}\text{, }y=7+10\beta -8\beta ^{2}\text{, }z=7+10\beta -8\beta ^{2}\text{, }a=d\text{ and }c=d\text{ and }b=d\text{ and }\left(\beta =\frac{-\sqrt{81-8d}+5}{8}\text{ or }\beta =\frac{\sqrt{81-8d}+5}{8}\right)\text{ and }d\leq \frac{81}{8}$$