tìm GTNN của: A= x ²+4x+5 B= 4x ²-4x+16 C=25x-10x+11 mn giúp mk với ạ Cám ơn mn 22/08/2021 Bởi Melanie tìm GTNN của: A= x ²+4x+5 B= 4x ²-4x+16 C=25x-10x+11 mn giúp mk với ạ Cám ơn mn
`A=x^2+4x+5=x^2+2.2.x+2^2+1` `=(x+2)^2+1` $\text{Có: $(x+2)^2$ ≥ 0 ∀ x}$ `⇒(x+2)^2+1≥1∀x` $\text{Dấu “=” xảy ra}$ `⇔x+2=0⇔x=-2` $\text{Vậy Min A = 1 khi x = -2}$ `B=4x^2-4x+16=(2x)^2-2.2x+1+15` `=(2x+1)^2+15` $\text{Có: $(2x+1)^2$ ≥ 0 ∀ x}$ `⇒(2x+1)^2+15≥15∀x` $\text{Dấu “=” xảy ra}$ `⇔2x+1=0⇔x=-1/2` $\text{Vậy Min B = 15 khi x = $\dfrac{-1}{2}$}$ `C=25x^2-10x+11=(5x)^2-2.5x+1+10` `=(5x-1)^2+10` $\text{Có: $(5x-1)^2$ ≥ 0 ∀ x}$ `⇒(5x-1)^2+10≥10∀x` $\text{Dấu “=” xảy ra}$ `⇔5x-1=0⇔x=1/5` $\text{Vậy Min C = 10 khi x = $\dfrac{1}{5}$}$ Bình luận
`A=x^2+4x+5=x^2+2.2.x+2^2+1`
`=(x+2)^2+1`
$\text{Có: $(x+2)^2$ ≥ 0 ∀ x}$
`⇒(x+2)^2+1≥1∀x`
$\text{Dấu “=” xảy ra}$
`⇔x+2=0⇔x=-2`
$\text{Vậy Min A = 1 khi x = -2}$
`B=4x^2-4x+16=(2x)^2-2.2x+1+15`
`=(2x+1)^2+15`
$\text{Có: $(2x+1)^2$ ≥ 0 ∀ x}$
`⇒(2x+1)^2+15≥15∀x`
$\text{Dấu “=” xảy ra}$
`⇔2x+1=0⇔x=-1/2`
$\text{Vậy Min B = 15 khi x = $\dfrac{-1}{2}$}$
`C=25x^2-10x+11=(5x)^2-2.5x+1+10`
`=(5x-1)^2+10`
$\text{Có: $(5x-1)^2$ ≥ 0 ∀ x}$
`⇒(5x-1)^2+10≥10∀x`
$\text{Dấu “=” xảy ra}$
`⇔5x-1=0⇔x=1/5`
$\text{Vậy Min C = 10 khi x = $\dfrac{1}{5}$}$