Answer:First, we can simplify the equation a^2 = 3a + 1 by subtracting 3a and 1 from both sides, to get:
a^2 - 3a - 1 = 0
Now we can factor the left side:
(a-1)(a+1) = 0
This equation tells us that either a-1 = 0 or a+1 = 0. So, a = 1 or a = -1.
Next, we can substitute these values into the expression (a+1/a)^2
For a = 1, (1+1/1)^2 = 2^2 = 4
For a = -1, (-1+1/(-1))^2 = 0^2 = 0
So, the value of (a+1/a)^2 is 4 when a = 1, and 0 when a = -1
Explanation: