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Posted: **Mon Jul 11, 2022 12:50 pm**

: 9 Let S A 5 B 2 A B E Q Prove That If Z Es Then There Exists Unique A B Q Such That Z A 5 B 2 You May A 1 (259.25 KiB) Viewed 32 times

9. Let S = {a√5 +b√2: a, b e Q}. Prove that if z ES, then there exists unique a, b € Q such that z = 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).