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compare P =2^a,Q =3, T=2^b, where a=\sqrt2 , 1+1/\sqrt2 (HOMC 2012 Q2)

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July 24, 2019
algebracomparison

Problem Statement

Compare the numbers P=2a,Q=3,T=2bP = 2^a,Q = 3, T = 2^b, where a=2,b=1+12a=\sqrt2 , b=1+\frac{1}{\sqrt2}
(A) P<Q<TP < Q < T, (B) T<P<QT < P < Q, (C) P<T<QP < T < Q, (D) T<Q<PT < Q < P, (E) Q<P<T Q < P < T
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