Let the initial quantity of grains be $x$. The first customer buys half of $x$ plus 3 kg, leaving $\frac{x}{2} - 3$ kg. The second customer then buys half of the remaining grains plus 3 kg, leaving $\frac{x}{4} - 3$ kg. The third customer buys half of what is left plus 3 kg, leaving 0 grains. Thus, we have the equation:
$\frac{x}{8} - 3 = 0 \implies x = 42$
If the set of all values of \( a \), for which the equation \( 5x^3 - 15x - a = 0 \) has three distinct real roots, is the interval \( (\alpha, \beta) \), then \( \beta - 2\alpha \) is equal to
If the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) has equal roots, where \( a + c = 15 \) and \( b = \frac{36}{5} \), then \( a^2 + c^2 \) is equal to .