If α and β are the roots of $3x^2-7x+3=0$, then α² − αβ + β² equals:

Rewrite the expression symmetrically: α² − αβ + β² = $(\alpha +\beta {)}^2-3$αβ. Here α + β = 7/3 and αβ = 3/3 = 1, so the value is 49/9 − 3 = 22/9. (31/9 subtracts 2αβ, which produces α² + β² instead; 40/9 subtracts αβ only once; 76/9 adds 3αβ.) The roots are (7 ± √13)/6 ≈ 1.7676 and 0.5657, and 3.1244 + 0.3200 − 1 ≈ 2.444 = 22/9.