a, $x^{2}$ - 8x + 34
= $x^{2}$ - 2.4x + $4^{2}$ + 18
= $(x-4)^{2}$ + 18 $\geq$ 18
Dấu "=" xảy ra ⇔ x - 4 = 0
⇔ x = 4
b, $4x^{2}$ + 12x + 31
= $(2x)^{2}$ + 2 . 3 . 2x + $3^{2}$ + 22
= $(2x+3)^{2}$ + 22 $\geq$ 22
Dấu "=" xảy ra ⇔ 2x + 3 = 0
⇔ 2x = - 3
⇔ x = -3/2
c, 9x^2-12x+29
= $(3x)^{2}$ - 2 . 2.3x + $2^{2}$ + 25
= $(3x-2)^{2}$ + 25 $\geq$ 25
Dấu "=" xảy ra ⇔ 3x - 2= 0
⇔ 3x = 2
⇔ x = 2/3
d, x^2 - x - 5
= $x^{2}$ - 2.$\frac{1}{2}$x + $\frac{1}{4}$ + $\frac{19}{4}$
= $(x-1/2)^{2}$ + $\frac{19}{4}$ $\geq$ $\frac{19}{4}$
Dấu "=" xảy ra ⇔ x = 1/2
