The numbers' escaping, through this square that is gaping!

Algebra Level 4

\[ \large \Big (a^{2}(b^{2} + 2) + 2ab + 1 \Big )^{2} = 6(a^{2} b + a)^{2}\]

Find the number of ordered pairs \((a,b)\) that satisfy the equation above such that \(a,b\) are positive real numbers.

Bonus: Find number of real numbers that satisfy the relation given above!

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