Toán Lớp 8: Tìm $\text{Min_{H}}$ biết: H = (x^2 – 2x + 2022)/(x^2)
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Toán Lớp 8: Tìm $\text{Min_{H}}$ biết: H = (x^2 – 2x + 2022)/(x^2)
Comments ( 2 )
H = (x² – 2x + 2022)/x²
= [(2021/2022).x²+(1/2022)x²-2x+2022]/x²
= (2021/2022) + $\frac{($\sqrt{1/2022}$ x – $\sqrt{2022}$ )²}{x²}$
= (2021/2022) + ($\frac{($\sqrt{1/2022}$ x – $\sqrt{2022}$ )}{x}$ )²
Dấu “=” xảy ra ⇔ $\sqrt{1/2022}$x = $\sqrt{2022}$
⇔ x = $\sqrt{2022}$ : $\sqrt{1/2022}$ = 2022
Vậy Min (H) = 2021/2022 tại x = 2022.
H=(x^2-2x+2022)/x^2
=(x^2 -2x+2022)/x^2 – 2021/2022 + 2021/2022
= (2022x^2 – 4044x + 2022^2 – 2021x^2)/(2022x^2) + 2021/2022
=(x^2 – 4044x +2022^2)/(2022x^2)+2021/2022
=(x^2-2.x.2022+2022^2)/(2022x^2)+2021/2022
=(x-2022)^2/(2022x^2)+2021/2022\ge 2021/2022 với mọi x
Dấu “=” xảy ra khi : x-2022=0<=>x=2022
Vậy min H=2021/2022<=>x=2022