Solve-for-a-a-2-1-a-a-1-a-2-

Question Number 6590 by Temp last updated on 04/Jul/16

Solve for a

\frac{a^{2} + 1}{a} = \frac{a}{1 - a^{2}}

Commented by nburiburu last updated on 04/Jul/16

1 - a^{4} = a^{2}

0 = a^{4} + a^{2} - 1

t = a^{2}

0 = t^{2} + t - 1

t_{1} = \frac{- 1 + \sqrt{1 + 4}}{2} = \frac{\sqrt{5} - 1}{2}

t_{2} = \frac{- 1 - \sqrt{1 + 4}}{2} = \frac{- \sqrt{5} - 1}{2}

a_{1} = \sqrt{t_{1}} = \sqrt{\frac{\sqrt{5} - 1}{2}}

a_{2} = - \sqrt{t_{1}} = - \sqrt{\frac{\sqrt{5} - 1}{2}}

a_{3} = \sqrt{t_{2}} = \sqrt{\frac{\sqrt{5} + 1}{2}} i

a_{4} = - \sqrt{t_{2}} = - \sqrt{\frac{\sqrt{5} + 1}{2}} i