a^2 = (7±√13)/2
Now it gets tricky:
7+√13 = (1+2√13+13)/2 = (1+√13)^2/2
a^2 = (7+√13)/2 = (1+√13)^2/4
a = ±1/2 (√13+1)
a = ±1/2 (√13-1)
Makes things kind of nasty, the factors are
1/16 (±2x + √13 ± 1)
where all 4 combinations of + and - are used.
substitute u=a^2, then
and try to factorize.
However, check you question to see if there is a typo. The above expression in u does not have rational factors.
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