Solve b_{2}-1(frac{1+sqrt{5}}{2})+b_{2}(frac{1-sqrt{5}}{2})^n

$$b _ { 2 } - 1 ( \frac { 1 + \sqrt { 5 } } { 2 } ) + b _ { 2 } ( \frac { 1 - \sqrt { 5 } } { 2 } ) ^ { n }$$

Factor

$$\frac{2b_{2}\times \left(\frac{1-\sqrt{5}}{2}\right)^{n}+2b_{2}-\sqrt{5}-1}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{2b_{2}-\left(1+\sqrt{5}\right)+2b_{2}\times \left(\frac{1-\sqrt{5}}{2}\right)^{n}}{2}$$

Evaluate

$$b_{2}\times \left(\frac{1-\sqrt{5}}{2}\right)^{n}+b_{2}-\frac{\sqrt{5}}{2}-\frac{1}{2}$$