Question

If $a-b-2=0$ and $a^3-b^3-6ab=k$ then find the value of $k$.

Answer 1

Given, $a-b-2=0$......(1) and $a^3-b^3-6ab=k$.....(2).

From (1) we get,

$a-b=2$

Cubing both sides we get,

$a^3-b^3-3ab(a-b)=2^3$

or, $a^3-b^3-6ab=8$ [ Since $a-b=2$]

Comparing this with (2) we get, $k=8$.