mk nha,tk mk

 m cũng hết lượt rùi

\(A=\frac{x^2-2x+2007}{2007x^2}=\frac{2006}{2007^2}+\frac{x^2-4014x+2007^2}{2007^2x^2}=\frac{2006}{2007^2}+\frac{\left(x-2007\right)^2}{2007^2x^2}\ge\frac{2006}{2007^2}\)

Dấu ''='' xảy ra \(\Leftrightarrow\) x = 2007

\(A=\frac{2007x^2-2x.2007+2007^2}{2007x^2}\)

\(=\frac{x^2-2x.2007+2007^2}{2007x^2}+\frac{2006x^2}{2007x^2}\)

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

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

`Q(x)=0`

`<=>x^4+3x^2+1=0

Vì `x^4>=0,x^2>=0`

`=>x^4+3x^2>=0`

`=>x^4+3x^2+1>=1>0`

`=>` ko có no

\(x\div\frac{1}{2}+x\div\frac{1}{4}+x\div\frac{1}{8}+x=960\)

        \(x\times2+x\times4+x\times8+x=960\)

                   \(x\times\left(2+4+8+1\right)=960\)

                                                  \(x\times15=960\)

                                                              \(x=960\div15\)

                                                              \(x=64\)

Sửa đề: \(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)

ĐKXĐ: x>=1

\(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)

=>\(\sqrt{\left(x-1\right)\left(x^3+x^2+x+1\right)}-\sqrt{x^3+x^2+x+1}-\sqrt{x-1}+1=0\)

=>\(\left(\sqrt{x-1}-1\right)\left(\sqrt{x^3+x^2+x+1}-1\right)=0\)

TH1: \(\sqrt{x-1}-1=0\)

=>\(\sqrt{x-1}=1\)

=>x-1=1

=>x=2(nhận)

TH2: \(\sqrt{x^3+x^2+x+1}-1=0\)

=>\(\sqrt{x^3+x^2+x+1}=1\)

=>\(x^3+x^2+x+1=1\)

=>\(x^3+x^2+x=0\)

=>\(x\left(x^2+x+1\right)=0\)

mà x>=1

nên x∈∅

\(\left(\dfrac{1}{2^2}-1\right)\times\left(\dfrac{1}{3^2-1}\right)\times\left(\dfrac{1}{4^2}-1\right)\times...\times\left(\dfrac{1}{100^2}-1\right)\)

\(=\dfrac{3}{2^2}\times\dfrac{8}{3^2}\times\dfrac{15}{4^2}\times...\times\dfrac{100^2-1}{100^2}\)

\(=\dfrac{1\times3}{2\times2}\times\dfrac{2\times4}{3\times3}\times\dfrac{3\times5}{4\times4}\times...\times\dfrac{99\times101}{100\times100}\)

\(=\dfrac{1\times2\times3\times...\times99}{2\times3\times4\times...\times100}\times\dfrac{3\times4\times5\times...\times101}{2\times3\times4\times...\times100}\)

\(=\dfrac{1}{100}\times\dfrac{101}{2}\)

\(=\dfrac{101}{200}\)

\(\left(\dfrac{1}{2^2}-1\right)\cdot\left(\dfrac{1}{3^2}-1\right)\cdot...\cdot\left(\dfrac{1}{100^2}-1\right)\)

\(=\dfrac{-3}{4}\cdot\dfrac{-8}{3}\cdot...\cdot\dfrac{-9999}{10000}\)

\(=\dfrac{1\cdot\left(-3\right)}{2\cdot2}\cdot\dfrac{2\cdot\left(-4\right)}{3\cdot3}\cdot...\cdot\dfrac{99\cdot\left(-101\right)}{100\cdot100}\)

\(=\dfrac{1\cdot2\cdot3\cdot...\cdot99}{2\cdot3\cdot4\cdot...\cdot100}\cdot\dfrac{\left(-3\right)\cdot\left(-4\right)\cdot...\cdot\left(-101\right)}{2\cdot3\cdot4\cdot...\cdot100}\)

Ở tử số phân số bên phải có số thừa số là: \(101-3+1=99\)

99 là số lẻ nên tử số vế phải sẽ cho ra số âm.

\(=\dfrac{1\cdot2\cdot3\cdot...\cdot99}{2\cdot3\cdot4\cdot...\cdot100}\cdot\dfrac{3\cdot4\cdot5\cdot...\cdot\left(-101\right)}{2\cdot3\cdot4\cdot...\cdot100}\)

\(=\dfrac{1\cdot\left(-101\right)}{100\cdot2}\)

\(=\dfrac{-101}{200}\)

Sao

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