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`3.` tìm GTNN
`a. x^2 - 2x + 5 = x^2 - 2x.1 + 1 + 4 =(x - 1)^2 + 4`
vì `(x - 1)^2 ≥ 0 ∀ x` `=> (x - 1)^2 + 4 ≥ 4`
Dấu bằng xảy ra `<=> x = 1 => Min P = 4 ⇔ x = 1`
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`b. M = 2x^2 - 6x = 2(x^2 -3x) = 2.(x^2 - 2.x.3/2 + 9/4)-9/2 = 2.(x-3/2)^2 - 9/2 `
vì `2.(x-3/2)^2 ≥ 0 ∀ => 2.(x-3/2)^2 - 9/2 ≥ - 9/2`
Dấu bằng xảy ra `<=> x = 3/2 => Min M = -9/2 ⇔ x = 3/2`
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`c. N = x^2 - 20x + 101 = = x^2 - 2.x.10 + 100 + 1 = (x - 10)^2 + 1 ≥ 1 `
Dấu bằng xảy ra `<=> x = 10 => Min N = 1 ⇔ x =10`
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`d. O = 4a^2 + 4a + 2`
`= (2a)^2 + 2.2a + 1 + 1= (2a + 1)^2 + 1 ≥1`
Dấu bằng xảy ra `<=> x = -1/2 => Min O = 1 ⇔ x =-1/2`
