MathematicsMedium19×since 2002Q5039Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be (103,73)\left( {{{10} \over 3},{7 \over 3}} \right)(310,37). If α\alphaα, β\betaβ are the roots of the equation ax2+bx+1=0a{x^2} + bx + 1 = 0ax2+bx+1=0, then the value of α2+β2−αβ{\alpha ^2} + {\beta ^2} - \alpha \betaα2+β2−αβ is :A69256{{69} \over {256}}25669B71256{{71} \over {256}}25671C−71256- {{71} \over {256}}−25671D−69256- {{69} \over {256}}−25669Check answerSkip