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Solve the system xy = 1, x + y =a
by using the identity

(x - y/2)^2 = (x + y/2)^2 - xy

mmmh, can't quite see how that helps

I would just do:
y = 1/x
sub into 2nd
x + 1/x = a
x^2 + 1 = ax
x^2 - ax + 1 = 0

x = (a ± √(a^2 - 4) )/2
y = 2/(a ± √(a^2 - 4) )

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