2b = a + c ${{2a + 2} \over 3} = {{10} \over 3}$ and ${{2b + c} \over 3} = {7 \over 3}$ a = 4, $\left\{ \matrix{ 2b + c = 7 \hfill \cr 2b - c = 4 \hfill \cr} \right\}$, solving $b = {{11} \over 4}$ $c = {3 \over 2}$ $\therefore$ Quadratic Equation is $4{x^2} + {{11} \over 4}x + 1 = 0$ $\therefore$ The value of ${\alpha ^2} + {\beta ^2} - \alpha \beta$ = ${\alpha ^2} + {\beta ^2} + 2\alpha \beta - 3\alpha \beta$ = ${(\alpha + \beta )^2} - 3\alpha \beta$ $= {{121} \over {256}} - {3 \over 4} = - {{71} \over {256}}$