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As far as the roots go, 20' away probably takes the roots out of the picture. The only way they'd mess with your A/G pool is if they broke the ground surface. As long as no roots break the surface within ~10' of the proposed pool, you'll be fine for the life of the pool.

Moles, on the other hand, can and will tunnel under an A/G pool causing 'sink lines' which will overstress the liner. I can't think of any practical way to shield the pool area from mole invasion, so I'd say you need to eliminate them.

HTH