36One more thing, this is an RMO 2007 question if someone can give a simple solution other than the one posted above then, i'll be grateful...
Find all pairs (a,b) of real numbers such that whenever α is a root of x2 + ax + b = 0, α2 - 2 is also a root of the equation.
I am confused with the solution of this question...
case1 : When α = β
So there is only one possiblity
α = α2 - 2
so, we get (a,b) = (-4,4) and (2,1)
Case2: When α ≠β
So there are four possiblities
1. α = α2 - 2 and β = β2 - 2
2. α = β2 - 2 and β = α2 - 2
3. α = α2 - 2 = β2 - 2 and α ≠β
4. β = α2 - 2 = β2 - 2 and α ≠β
How are these four possiblities logical. Please explain [experts needed.....]
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