How do you simplify #(sqrt5-2)(sqrt5+2)#?

1 Answer
Mar 17, 2018

Answer:

See a solution process below:

Explanation:

Use this rule for quadratics for this special case:

#(color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - color(blue)(y)^2#

Let:

  • #color(red)(sqrt(5)) = color(red)(x)#
  • #color(blue)(2) = color(blue)(y)#

Substitute as:

#(color(red)(sqrt(5)) + color(blue)(2))(color(red)(sqrt(5)) - color(blue)(2)) =>#

#(color(red)(sqrt(5)))^2 - color(blue)(2)^2 =>#

#5 - 4 =>#

#1#