(In reply to

Solution by David Shin)

Haha, oops, the square roots and cubes don't work for some reason. Here's a better version:

From the equations (1+sqrt(2))^3=(7+5sqrt(2)) and (1-sqrt(2))^3=(7-5sqrt(2)), we deduce that a = (1+sqrt(2)) + (1-sqrt(2)) = 2.