If the two equations X & # 178; + (a + 1) x + A & # 178; = 0 are reciprocal to each other, a =?

If the two equations X & # 178; + (a + 1) x + A & # 178; = 0 are reciprocal to each other, a =?

Weida theorem
x1+x2=-(a+1)
x1x2=a²
The reciprocal is x1x2 = 1
a²=1
a=±1
If there is a solution, then △ = A & # 178; + 2A + 1-4a & # 178; > = 0
3a²-2a-1