If a - b = 3 and $a^3 - b^3 = 999$, then find the value of $a^2 - b^2$.

63

(a - b)³ = a³ - b³ - 3ab(a-b)

If a - b = 3

$a^3 - b^3 = 999$,

then find the value of $a^2 - b^2$

(3)³ = 999 - 3ab(3)

27 = 999 - 9ab

ab = \(\frac{972}{9}\) = 108

We know that,

If x - y  = n

then, x + y  = \(\sqrt {n^2 + 4xy}\)

a + b = \(\sqrt {3^2 + 4(108)}\)

a + b = \(\sqrt {9 + 432}\)

a + b = 21

Now,

a² - b² = (a + b) (a – b)

a² - b² = ( 3) (21) = 63