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Question: problem 2 let f be the set a bv5 a...

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Problem 2. Let F be the set a bv5: a, b E Q), with the usual definitions of addition and multiplication (a) Let p-, + vs (this number is called the golden ratio). Expres y 2 and 1/p in the form a bv5 with a, b eQ (b) Prove that F is a field Note: We take it as a known fact that the usual addition and multiplication of real numbers are commutative, associative, and distributive. You can also use the fact that the square root of a prime number is irrational; this is proved the same way as the irrationality of v2.
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