Question

If a = to 3 minus under root 5 upon 3 + under root 5 and b equals to 3 + under root 5.3 minus under root 5 find a square minus b square

Answer 1

a = 3-√5 / 3+√5 and b = 3+√5 /3-√5

therefore ( a+b ) ( a - b ) =

[( 3-√5 / 3+√5 + 3+√5 /3-√5 ) ] [( 3-√5 / 3+√5 - 3+√5 /3-√5 )]

=[ ( 3 - √5 )^2 + ( 3 +√5 )^2/ 9 - 5] [ ( 3 - √5 )^2 - ( 3 +√5 )^2/ 9 - 5]

=[ 9 - 6√5 + 5 + 9+6√5+5 / 4] [ 9 - 6√5 + 5 - 9 -6√5 - 5 / 4]

= [28/4 ] [ - 12√5/4]

= 7 ×(-3√5)

( a+b ) ( a - b ) = -21√5

a^2 - b^2 = -21√5

Answer 2

Answer:-21√5

Step-by-step explanation:

a = 3-√5 / 3+√5 and b = 3+√5 /3-√5

therefore ( a+b ) ( a - b ) =

[( 3-√5 / 3+√5 + 3+√5 /3-√5 ) ] [( 3-√5 / 3+√5 - 3+√5 /3-√5 )]

=[ ( 3 - √5 )^2 + ( 3 +√5 )^2/ 9 - 5] [ ( 3 - √5 )^2 - ( 3 +√5 )^2/ 9 - 5]

=[ 9 - 6√5 + 5 + 9+6√5+5 / 4] [ 9 - 6√5 + 5 - 9 -6√5 - 5 / 4]

= [28/4 ] [ - 12√5/4]

= 7 ×(-3√5)

( a+b ) ( a - b ) = -21√5

a^2 - b^2 = -21√5