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# FP3 Group Question watch

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1. H denotes the set of numbers of the form a + b 5, where a and b are rational. The numbers are
combined under multiplication.
(i) Show that the product of any two members of H is a member of H .
[2]
It is now given that, for a and b not both zero, H forms a group under multiplication.
(ii) State the identity element of the group.
[1]

(iii) Find the inverse of a + b 5.
[2]
(iv) With reference to your answer to part (iii), state a property of the number 5 which ensures that
every number in the group has an inverse.
[1]
I'm stuck on part iv). The answer says that it is because 5 is prime or sqrt5 is irrational, however I'm not sure why this is relevant.

(The answer to part (iii) was a/(a^2-5b^2) - (b/(a^2-5b^2))sqrt5 )

Thanks
2. Notice that there is always an inverse if the denominators in the expression are not zero; but why can't equal zero?, with .

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Updated: May 23, 2010
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