Bài 3:
` a) ` ` M = x^2 - 4x + 5 `
` M = x^2 - 4x + 4 + 1 `
` M = (x - 2)^2 + 1 `
Vì ` (x - 2)^2 ≥ 0 `
` => (x - 2)^2 + 1 ≥ 1 `
Vậy ` Mi n_M = 1, ` dấu $"="$ xảy ra khi: ` x - 2 = 0 <=> x = 2 `
` b) ` ` N = y^2 - y - 3 `
` N = y^2 - 2 . y . 1/2 + 1/4 - (13)/4 `
` N = (y - 1/2)^2 - (13)/4 `
Vì ` (y - 1/2)^2 ≥ 0 `
` => (y - 1/2)^2 - (13)/4 ≥ - (13)/4 `
Vậy ` Mi n_N = - (13)/4 , ` dấu $"="$ xảy ra khi: ` y - 1/2 = 0 <=> y = 1/2 `
Bài 4:
` a) ` ` A = -x^2 + 4x + 2 `
` A = -(x^2 - 4x + 4 - 6) `
` A = -(x - 2)^2 + 6 `
Vì ` (x - 2)^2 ≥ 0 `
` => -(x - 2)^2 ≤ 0 `
` => -(x - 2)^2 + 6 ≤ 6 `
Vậy ` Max_A = 6, ` dấu $"="$ xảy ra khi: ` x - 2 = 0 <=> x = 2 `
` b) ` ` B = x - x^2 + 6 `
` B = -(x^2 - x - 6) `
` B = -(x^2 - 2 . x . 1/2 + 1/4 - (25)/4) `
` B = -(x - 1/2)^2 + (25)/4 `
Vì ` (x - 1/2)^2 ≥ 0 `
` => -(x - 1/2)^2 ≤ 0 `
` => -(x - 1/2)^2 + (25)/4 ≤ (25)/4 `
Vậy ` Max_B = (25)/4 , ` dấu $"="$ xảy ra khi: ` x - 1/2 = 0 <=> x = 1/2 `
