Question: Let x be a number with x > 1. Use direct proof to prove that a number 'a' is strictly between 1 and sqrt(x) if

Let x be a number with x > 1. Use direct proof to prove that a number 'a' is strictly between 1 and sqrt(x) if and only if (x/a) is strictly between sqrt(x) and x. Assume that 1 < sqrt(x) < x.

*HINT: Start from p --> q. Assume that 1 < a < sqrt(x) and try to prove sqrt(x) < (x/a) < x. Then, how can you get sqrt(x) < (x/a) < x from 1 < a < sqrt(x)?

Clearly label each step and law.

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