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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10, SAT-II.
What is the minimum of the expression:
(by C. Ionescu-Tiu)
Notice that, by adding a constant number, we can force a perfect square out of:
and similarly for b.
Therefore, subtracting back what we added in order to force the perfect squares:
Since the minimum value of any square is zero, the expression always satisfies:
Therefore, the minimum value of the expression E is 4.5.