áp dụng BĐT côsi ta có : \(\frac{x^2}{y^2}+\frac{y^2}{x^2}>=2\sqrt{\frac{x^2}{y^2}\cdot\frac{y^2}{x^2}}=2;\frac{x}{y}+\frac{y}{x}>=2\)

=> B>= 2-3*2+5=1

Dấu bằng khi x=y=1

2012p=2012(x^2-2x+2012)/x^2

2012p=(2012x^2-2.2012.x+2012^2)/x^2

2012p=(2011x^2+(x^2-2.2012.x+2012^2))/x^2

2012p=2011+(x-2012)^2/x^2 >=2011

suy ra GTNN của 2012p là 2011

GTNN của p là 2011/2012

xảy ra khi x=2012

\(A=\frac{x^2-x+2}{x^2}\)

\(A=\frac{x^2}{x^2}-\frac{x}{x^2}+\frac{2}{x^2}\)

\(A=1-\frac{1}{x}+2\cdot\left(\frac{1}{x}\right)^2\)

Đặt \(\frac{1}{x}=a\)

\(A=1-a+2a^2\)

\(A=2\left(a^2-\frac{a}{2}+\frac{1}{2}\right)\)

\(A=2\left(a^2-2\cdot a\cdot\frac{1}{4}+\frac{1}{16}+\frac{7}{16}\right)\)

\(A=2\left[\left(a-\frac{1}{4}\right)^2+\frac{7}{16}\right]\)

\(A=2\left(a-\frac{1}{4}\right)^2+\frac{7}{8}\ge\frac{7}{8}\forall a\)

Dấu "=" xảy ra \(\Leftrightarrow a=\frac{1}{4}\Leftrightarrow\frac{1}{x}=\frac{1}{4}\Leftrightarrow x=4\)

A = \(\dfrac{x^2-2x+2020}{2021x^2}\)

= \(\dfrac{2020x^2-2.2020.x+2020^2}{2021.2020x^2}\)

\(=\dfrac{2019x^2}{2021.2020x^2}+\dfrac{x^2-2.2020.x+2020^2}{2021.2020x^2}\)

= \(\dfrac{2019}{2021.2020}+\dfrac{\left(x-2020\right)^2}{2021.2020x^2}\ge\dfrac{2019}{2021.2020}\)

Dấu "=" xảy ra <=> x - 2020 = 0

                       <=> x = 2020

Vậy minA = \(\dfrac{2019}{2021.2020}\)đạt được tại x = 2020

Ai giúp mik vs

Huhu ai giúp vs

hi sư huynh đệ mới lớp 6

\(A=\frac{x^2-2x+2007}{2007x^2},\left(x\ne0\right)\)

\(A=\frac{2007x^2-2x.2007+2007^2}{2007x^2}=\frac{x^2-2x.2007+2007^2}{2007x^2}+\frac{2006x^2}{2007x^2}=\) \(\frac{\left(x-2007\right)^2}{2007x^2}+\frac{2006}{2007}\ge\frac{2006}{2007}\)

\(A_{min}=\frac{2006}{2007}\) khi \(x-2007=0\) hay \(x=2007\)

Chúc bạn học tốt !!!

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12007" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">12007 - 22007x" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">22007x + 1x2" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">1x2

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<=> x = 2007

Vậy x = 2007 thì Amin

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