9. Let S = {a√5 +b√2: a,b € Q}. Prove that if ze S, then there exists unique a, b € Q such that x = a√5 +b√2. You may as

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9 Let S A 5 B 2 A B Q Prove That If Ze S Then There Exists Unique A B Q Such That X A 5 B 2 You May As 1 (13.67 KiB) Viewed 27 times

9. Let S = {a√5 +b√2: a,b € Q}. Prove that if ze S, then there exists unique a, b € Q such that x = a√5 +b√2. You may assume that √2, √5, and their quotients are all irrational. You may also assume the zero-product property (If ab= 0, then a = 0 or b= 0).