Let $$\alpha ,\beta $$ and $$\gamma ,\delta $$ be the roots of the equations $${x^2} + ax + b = 0$$

and $${x^2} + bx + a = 0$$ respectively.

$$\therefore$$ $$\alpha + \beta = - a,\alpha \beta = b$$

and $$\gamma + \delta = - b,\gamma \delta = a.$$

Given $$\left| {\alpha - \beta } \right| = \left| {\gamma - \delta } \right|$$

$$ \Rightarrow {\left( {\alpha - \beta } \right)^2} = {\left( {\gamma - \delta } \right)^2}$$

$$ \Rightarrow {\left( {\alpha + \beta } \right)^2} - 4\alpha \beta = {\left( {\gamma + \delta } \right)^2} - 4\gamma \delta $$

$$ \Rightarrow {a^2} - 4b = {b^2} - 4a$$

$$ \Rightarrow \left( {{a^2} - {b^2}} \right) + 4\left( {a - b} \right) = 0$$

$$ \Rightarrow a + b + 4 = 0$$

( as $$a \ne b$$ )