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Can, we proceed this way.
If it is a perfect square, essentially, its roots have been reduced to 2 from 4.
Then, if p and q are the roots, then,
p.p.q.q = 1 , 2p+2q = -a , 2p.p + 2q.q + 4pq = b
and another equation , summantion of roots taken three at a time = 8
So we have 4 equations and 4 variables
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