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

Algebra Level 5

(a2(b2+2)+2ab+1)2=6(a2b+a)2 \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)(a,b) that satisfy the equation above such that a,ba,b are positive real numbers.

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

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