Question

If a – b = 7 and a2 + b2 = 85, then find the value of a3 - b³​

Answer 1

Answer:

your answer attached in the photo

Answer 2

Answer:

721

Step-by-step explanation:

$a - b = 7$

${a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab$

$85 = {(7)}^{2} + 2ab$

$85 = 49 + 2ab$

$85 - 49 = 2ab$

$36 = 2ab$

$ab = 18$

${a}^{3} - {b}^{3} = {(a - b)}^{3} + 3ab(a - b)$

$= {(7)}^{3} + 3 \times 18 \times (7)$

$= 343 + 378$

$= 721$