Give a proof of the following implication: Let x be an arbritrary real number.
If 2x^2 + 2/x^2 = pi, then x^pi + x^(log10) = e^pi*pi^e
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So if is real, the minimum value of is , and therefore has no real solutions.
So if is the propositional function: and is the propositional function :
, since is always false
i.e. for all real values of .