36 & 81f-401-2 1 and α +-, is an odd integer then number of possible

1.	36 & 81f-401-2 1 and α +-, is an odd integer then number of possible values of α isa +1
Answer» 4a/(a²+1)≥1=> 4/(a²+1/a) ≥1=> 4/(a+1/a) ≥ 1=> 4 ≥ (a+1/a) => a+1/a ≤ 4 but also, a+1/a is always ≥ 2 so, only possible odd value between 2 and 4, is 3 oh i solved for value of a+1/a, here it is asking value of a so just solve a+1/a = 3 => a²+1 = 3a=> a²-3a+1 = 0 here ∆ = (-3)²-4 = 9-4 =√5 so, 2 irrational real roots.. of a exist. => a = (3±√5)/2 or a = (3+√5)/2 and (3-√5)/2 2 solutions edit - the process is perfectly correct.. do just assume that it is wrong by seeing the answer. now I am unable to understand

36 & 81f-401-2 1 and α +-, is an odd integer then number of possible values of α isa +1

Answer»

4a/(a²+1)≥1=> 4/(a²+1/a) ≥1=> 4/(a+1/a) ≥ 1=> 4 ≥ (a+1/a)

=> a+1/a ≤ 4

but also, a+1/a is always ≥ 2

so, only possible odd value between 2 and 4, is 3

oh i solved for value of a+1/a, here it is asking value of a

so just solve a+1/a = 3 => a²+1 = 3a=> a²-3a+1 = 0

here ∆ = (-3)²-4 = 9-4 =√5 so, 2 irrational real roots.. of a exist. => a = (3±√5)/2 or a = (3+√5)/2 and (3-√5)/2

2 solutions

edit - the process is perfectly correct.. do just assume that it is wrong by seeing the answer.

now I am unable to understand