How do you simplify #(sqrta-sqrt5)^2#?

1 Answer
May 17, 2018

Answer:

See a solution process below:

Explanation:

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)#