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(Solved): 13. Show that every nonzero element in the set \( Q(\sqrt{5})=\{a+b \sqrt{5}: a, b \in Q\} \) has a ...





13. Show that every nonzero element in the set \( Q(\sqrt{5})=\{a+b \sqrt{5}: a, b \in Q\} \) has a multiplicative inverse th
13. Show that every nonzero element in the set \( Q(\sqrt{5})=\{a+b \sqrt{5}: a, b \in Q\} \) has a multiplicative inverse that is also in \( Q(\sqrt{5}) \).


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