If a is the root of the equation x² - (a + b)x + k = 0, find the value of k.

Since, a is the root of the equation x² - (a + b)x + k = 0 , x = a satisfies the given equation.

Substituting x = a in the given equation:

$\Rightarrow a^2 - (a+b)a + k = 0 \\[0.5em] \Rightarrow a^2 - (a^2 + ab) + k = 0 \\[0.5em] \Rightarrow a^2 - a^2 - ab + k = 0 \\[0.5em] \Rightarrow k - ab = 0 \\[0.5em] \Rightarrow k = ab$

Hence, the value of k is ab.