Given the numbers a=square root(5-square root21) and b=square root(5+square root21), what is the product of a^-1*b^-1?

It is given that a = sqrt(5 - sqrt 21) and b = sqrt(5 +
sqrt 21)

We have to determine a^(-1) * b^(-1) =
1/(a*b)

a*b = [sqrt(5 - sqrt 21)][sqrt(5 + sqrt
21)]

=> sqrt [(5 - sqrt 21)(5 + sqrt
21)]

=> sqrt [ 5^2 - (sqrt
21)^2]

=> sqrt [25 -
21]

=> sqrt 4

=>
+/-2

1/(a*b) =
+/-1/2

The product a^-1*b^-1 is 1/2 or
-1/2