$\text{Câu 20:}$
`S=4x-2x^2+1`
`=-(2x^2-4x-1)`
`=-(2x^2-2.\sqrt{2}.x.\sqrt{2}+2-3)`
`=-[(\sqrt{2}x-\sqrt{2})^2-3]`
`=-(\sqrt{2}x-\sqrt{2})^2+3`
$\text{Có: $(\sqrt{2}x-\sqrt{2})^2$ ≥ 0 ∀ x}$
`⇒-(\sqrt{2}x-\sqrt{2})^2 ≤ 0 ∀ x`
`⇒-(\sqrt{2}x-\sqrt{2})^2+3 ≤ 3∀x`
`⇒Max S = 3`
$\text{Câu 21:}$
`P=x^2-4x+5`
`=x^2-4x+4+1`
`=(x-2)^2+1`
$\text{Có: $(x-2)^2$ ≥ 0 ∀ x}$
`⇒(x-2)^2+1≥1∀x`
`⇒ Mi n P = 1`
$\text{Câu 22:}$
`x^2+y^2-2x+4y+8`
`=x^2-2x+1+y^2+4y+4+3`
`=(x-1)^2+(y+2)^2+3`
$\text{Có: $(x-1)^2$ ≥ 0 ∀ x; $(y+2)^2$ ≥ 0 ∀ x}$
`⇒(x-1)^2+(y+2)^2 ≥ 0 ∀x`
`⇒(x-1)^2+(y+2)^2+3≥3∀x`
$\text{⇒ Min biểu thức = 3}$
$\text{Câu 23:}$
`3x^2+3x+x^3+1`
`=(x+1)^3(HĐT)`
