The rule for this special form of quadratic equation is:
#(color(red)(x) - color(blue)(y))^2 = (color(red)(x) - color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - 2color(red)(x)color(blue)(y) + color(blue)(y)^2#
Substitute:
#color(red)(sqrt(a))# for #color(red)(x)#
#color(blue)(sqrt(5))# for #color(blue)(y)#
Giving:
#(color(red)(sqrt(a)) - color(blue)(sqrt(5)))^2 =>#
#(color(red)(sqrt(a)) - color(blue)(sqrt(5)))(color(red)(sqrt(a)) - color(blue)(sqrt(5))) =>#
#(color(red)(sqrt(a)))^2 - 2color(red)(sqrt(a))color(blue)(sqrt(5)) + (color(blue)(sqrt(5)))^2 =>#
#color(red)(a) - 2sqrt(color(red)(a)color(blue)(5)) + color(blue)(5)#
