The osmotic pressure (\( \pi \)) for a solution is given by the formula:
\[ \pi = \frac{nRT}{V} \] where:
\( n \) is the number of moles of solute,
\( R \) is the gas constant,
\( T \) is the temperature,
\( V \) is the volume of the solution.
For non-electrolyte (A) and glucose, the osmotic pressures are the same, so we can equate the osmotic pressures: \[ \frac{12 / M_A}{1} = 0.05 \times 1 \] where \( M_A \) is the molar mass of A, and 12 g is the mass of A. Simplifying the equation: \[ \frac{12}{M_A} = 0.05 \quad \Rightarrow \quad M_A = \frac{12}{0.05} = 240 \, \text{g/mol}. \] Thus, the molecular mass of A is 240 g/mol.
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.