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

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Question Number 6590 by Temp last updated on 04/Jul/16
Solve for a ((a^2 +1)/a)=(a/(1−a^2 ))
Solveforaa2+1a=a1−a2
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 =((−1+(√(1+4)))/2)=(((√5)−1)/2) t_2 =((−1−(√(1+4)))/2)=((−(√5)−1)/2) a_1 =(√t_1 )=(√(((√5)−1)/2)) a_2 =−(√t_1 )=−(√(((√5)−1)/2)) a_3 =(√t_2 )=(√(((√5)+1)/2))i a_4 =−(√t_2 )=−(√(((√5)+1)/2))i
1−a4=a20=a4+a2−1t=a20=t2+t−1t1=−1+1+42=5−12t2=−1−1+42=−5−12a1=t1=5−12a2=−t1=−5−12a3=t2=5+12ia4=−t2=−5+12i

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