Toán TIM GTLL CUA BIEU THUC A a= √X – 2 chia X √X -8 01/12/2021 By Liliana TIM GTLL CUA BIEU THUC A a= √X – 2 chia X √X -8
đkxđ: `x≥0; x\ne 4` `A=(\sqrtx-2)/[x\sqrtx-8]` `A=(\sqrtx-2)/[(\sqrtx-2)(x+2\sqrtx+4)]` `A=1/(x+2\sqrtx+4)` `A=1/[(\sqrtx+1)^2+3]` Vì `\sqrtx≥0` `⇒(\sqrtx+1)^2+3≥1+3=4` `⇒A=1/[(\sqrtx+1)^2+1]≤1/4` Dấu `=` xảy ra `⇔\sqrtx=0⇒x=0` Vậy $Max_A=\dfrac{1}{4}⇔=0$ Trả lời
đkxđ: `x≥0; x\ne 4`
`A=(\sqrtx-2)/[x\sqrtx-8]`
`A=(\sqrtx-2)/[(\sqrtx-2)(x+2\sqrtx+4)]`
`A=1/(x+2\sqrtx+4)`
`A=1/[(\sqrtx+1)^2+3]`
Vì `\sqrtx≥0`
`⇒(\sqrtx+1)^2+3≥1+3=4`
`⇒A=1/[(\sqrtx+1)^2+1]≤1/4`
Dấu `=` xảy ra `⇔\sqrtx=0⇒x=0`
Vậy $Max_A=\dfrac{1}{4}⇔=0$