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DD
28 tháng 5 2021

\(M=x-2\sqrt{x-3}+1=x-3-2\sqrt{x-3}+1+3=\left(\sqrt{x-3}-1\right)^2+3\ge3\)

Dấu \(=\)khi \(\sqrt{x-3}-1=0\Leftrightarrow x=4\)

15 tháng 8 2021

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7 tháng 10 2018

Ta có \(\hept{\begin{cases}\sqrt{4x-4}\ge0\\\sqrt{25x-5}\ge0\\\sqrt{81x-81}\ge0\end{cases}}\)

Mà \(\sqrt{4x-4}+\sqrt{25x-25}+\sqrt{81x-81}=-1\)

Nên pt trên vô nghiệm

Bài toán: Cho ba số x,y,zx,y,z thỏa mãn x+y+z=0x+y+z=0 và x2+y2+z2=a2x2+y2+z2=a2....
Đọc tiếp

Bài toán: Cho ba số x,y,z" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x,y,z thỏa mãn x+y+z=0" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x+y+z=0 và x2+y2+z2=a2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x2+y2+z2=a2. Tính x4+y4+z4" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x4+y4+z4 theo a" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a.

 

 
1
27 tháng 7 2016

vì a+b+c=0==> x=-(y+z) ==> \(x^2=\left(y+z\right)^2\)

<=> \(x^2=y^2+2yz+z^2\)

<=> \(x^2-y^2-z^2=2yz\)

<=> \(\left(x^2-y^2-z^2\right)^2=4y^2z^2\)

<=>\(x^4+y^4+z^4=2x^2y^2+2y^2z^2+2z^2x^2\)

<=> \(2\left(x^4+y^4+z^4\right)=\left(x^2+y^2+z^2\right)^2=a^4\)

==> \(x^4+y^4+z^4=\frac{a^4}{2}\)

Cho biểu thức P=(√x−√y1+√xyx−y1+xy+√x+√y1−√xyx+y1−xy):(x+y+2xy1−xyx+y+2xy1−xy+1)a) Rút gọn Pb) Tính giá trị của P tại x=22+√322+3 c) Chứng minh:...
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Cho biểu thức P=(x&#x2212;y1+xy" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">xy1+xy+x+y1&#x2212;xy" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">x+y1xy):(x+y+2xy1&#x2212;xy" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">x+y+2xy1xy+1)

a) Rút gọn P

b) Tính giá trị của P tại x=22+3" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">22+3

 

c) Chứng minh: P≤1

 

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