a) x2 + x + 3 = (x2 + 2.x.\(\frac{1}{2}\) + \(\frac{1}{4}\)) + \(\frac{11}{4}\) = \(\left(x+\frac{1}{2}\right)^2+\frac{11}{4}\) \(\ge\) \(\frac{11}{4}\)
Vậy: GTNN là \(\frac{11}{4}\) (tại x = \(\frac{-1}{2}\))
b) x(x + 4) = x2 + 4x = (x2 + 2.x.2 + 4) - 4 = (x + 2)2 - 4 \(\ge\) -4
Vậy: GTNN là -4 <=> (x + 2)2 <=> x = -2)
c) (x - 1)(x + 3) - 1 = x2 + 3x - x - 3 - 1
= x2 + 2x - 4 = (x2 + 2.x.1 + 1) -5 = (x + 1)2 - 5 \(\ge\) -5
Vậy: GTNN là -5 <=> (x + 1)2 <=> x = -1)
d) 9x2 - 6x + 5 = (9x2 - 2.3x.1 + 1) + 4 = (3x - 1)2 + 4 \(\ge\) 4
Vậy: GTNN là 4 <=> (3x - 1)2 = 0 <=> x = \(\frac{1}{3}\)
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