Question: 9. Let S = {av5 + bv2 : a, b E Q}. Prove that if r E S, then there exists unique a, b E

9. Let S = {av5 + bv2 : a, b E

9. Let S = {av5 + bv2 : a, b E Q}. Prove that if r E S, then there exists unique a, b E Q such that = = av5 + bv/2. You may assume that v2, v5, and their quotients are all irrational. You may also assume the zero-product property (If ab = 0, then a = 0 or b = 0)

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