Find the value of $$a$$ in the following equation. (Given: $$a$$ < 10.)
$$\frac{{\left( {187 \div 17 \times a - 3 \times 3} \right)}}{{\left( {{8^2} - 9 \times 7 + {a^2}} \right)}} = 1$$

$$\eqalign{ & \frac{{\left( {187 \div 17 \times a - 3 \times 3} \right)}}{{\left( {{8^2} - 9 \times 7 + {a^2}} \right)}} = 1 \cr & 11a - 9 = 64 - 63 + {a^2} \cr & 11a - 9 = 1 + {a^2} \cr & {a^2} - 11a + 10 = 0 \cr & {a^2} - \left( {10 + 1} \right)a + 10 = 0 \cr & {a^2} - 10a - a + 10 = 0 \cr & a\left( {a - 10} \right) - 1\left( {a - 10} \right) = 0 \cr & \left( {a - 10} \right)\left( {a - 1} \right) = 0 \cr & a = 1,\,10{\text{ Answer}} \cr} $$