Question

a-b равно 2, ab равно 3, найти a3 - b3

Answer 1

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$
$\\ a - b = 2 \\ ab = 3 \\ {(a - b)}^{2} = {(2)}^{2} \\ {a}^{2} - 2ab + {b}^{2} = 4 \\ {a}^{2} + {b}^{2} = 4 + 2ab \\ {a}^{2} + {b}^{2} = 4 + 2 \times 3 \\ {a}^{2} + {b}^{2} = 10 \\ {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + 2ab + {b}^{2} ) = 2 \times (10 + 3) = 2 \times 13 = 26$