If $$16a^4 + 36a^2b^2 + 81b^4 = 91$$ and $$4a^2 + 9b^2 - 6ab = 13$$, then what is the value of $$3ab$$?

$$4a^2 + 9b^2 - 6ab = 13$$

$$(4a^2 + 9b^2 - 6ab)^2 = (13)^2$$

$$(\because(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ac))$$

$$(4a^2)^2 + (9b^2)^2 + (6ab)^2 +2(4a^2.9b^2 - 9b^2.6ab - 6ab.4a^2) = 169$$

$$16a^4 + 36a^2b^2 + 81b^4 + 2(36a^2b^2 - 54ab^3 - 24a^3b) = 169$$

$$91 + 2(36a^2b^2 - 54ab^3 - 24a^3b) = 169$$

$$36a^2b^2 - 54ab^3 - 24a^3b = \frac{169 - 91}{2}$$

$$36a^2b^2 - 54ab^3 - 24a^3b = 39$$

$$6ab(6ab - 9b^2 - 4a^2) = 39$$

$$6ab(-13) = 39$$

6ab = -3

3ab = -3/2