Question

If a+b=2 and ab= -24, find the values of (i) a³-b³ (ii) a³+b³​

Answer 1

Answer:

$a + b = 2 \\ {(a + b)}^{3} = 8 \\ {a}^{3} + {b}^{3 } + 3ab(a + b) = 8 \\ {a}^{3} + {b}^{3 } + 3( - 24)(2) = 8 \\ {a}^{3} + {b}^{3 } - 144 = 8 \\ {a}^{3} + {b}^{3 } = 144 + 8 = 152$

we know

${(a + b)}^{2} - {(a - b)}^{2} = 4ab \\ {2}^{2} - {(a - b)}^{2} = 4( - 24) \\ 4 - {(a - b)}^{2} = - 96 \\ {(a - b)}^{2} = 100 \\ a - b \: = 10 \\ cubing \: both \: sides \\ {a}^{3} - {b}^{3} - 3ab(a - b) = 1000 \\ {a}^{3} - {b}^{3} - 3( - 24)(10) = 1000 \\ {a}^{3} - {b}^{3} = 1000 - 720 = 280$