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KK
26 tháng 8 2021
Ohhh, tui hiểu r.
x2 - x + \(\dfrac{1}{4}\)
⇔ x2 - 2.\(\dfrac{1}{2}\).x + \(\left(\dfrac{1}{2}\right)^2\)
⇔ \(\left(x^2-\dfrac{1}{2}\right)^2\)
29 tháng 12 2018
\(A=\left(\frac{1}{x-1}-\frac{2x}{x\left(x^2+1\right)-\left(x^2+1\right)}\right):\left(\frac{x^2+1-2x}{x^2+1}\right)\)
\(A=\left(\frac{1}{x-1}-\frac{2x}{\left(x-1\right)\left(x^2+1\right)}\right).\frac{x^2+1}{x^2+1-2x}\)
\(A=\frac{x^2+1-2x}{\left(x-1\right)\left(x^2+1\right)}\frac{x^2+1}{x^2+1-2x}\)
\(A=\frac{1}{x-1}\)
2 tháng 4 2018
\(b)\) \(\left(2x-1\right)^{2012}=\left(2x-1\right)^{2010}\)
\(\Leftrightarrow\)\(\left(2x-1\right)^{2010}.\left(2x-1\right)^2=\left(2x-1\right)^{2010}\)
\(\Leftrightarrow\)\(\left(2x-1\right)^2=1\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}2x-1=1\\2x-1=-1\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=2\\2x=0\end{cases}}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{2}{2}\\x=\frac{0}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=0\end{cases}}}\)
Vậy \(x=0\) hoặc \(x=1\)
Chúc bạn học tốt ~
NH
2
H
6 tháng 6 2023
` @Answer`
`2,(7+3x-y)(7-3x+y)`
`=(7+3x)^2 - y^2`
`3, (6/5 - 5x)^2`
`=(6/5)^2 - 2 . 6/5 . 5x+ (5x)^2`
`= 36/25 - 12x + 25x^2`
Công thức :
`(x-y)(x+y) = x^2 - y^2`
`(x+y)^2=x^2+2xy+y^2`
`+,` Đề `1:(2x+y^2)` ngoài ngoặc có gì ạ ?
KV
6 tháng 6 2023
2)
(7 + 3x - y)(7 - 3x + y)
= [7 + (3x - y)][7 - (3x + y)]
= 7² - (3x - y)²
= 49 - (3x - y)²
= 49 - (9x² - 6xy + y²)
= 49 - 9x² + 6xy - y²
NN
15 tháng 4 2017
Tìm \(MAX\)
Ta có: \(\frac{2x+1}{x^2+2}=\frac{x^2+2-x^2+2x-1}{x^2+2}\)
\(=1-\frac{\left(x-1\right)^2}{x^2+2}\le1\)
Dấu "=" xảy ra khi \(\Leftrightarrow-\frac{\left(x-1\right)^2}{x^2+2}=0\Leftrightarrow x-1=0\Leftrightarrow x=1\)
Vậy GTLN của biểu thức là \(1\) tại \(x=1\)
Tìm \(MIN\)
Ta có: \(1-\frac{\left(x-1\right)^2}{x^2+2}=-\frac{1}{2}+\frac{3}{2}-\frac{\left(x-1\right)^2}{x^2+2}\)
\(=-\frac{1}{2}+\frac{3x^2+6-2x^2+4x-2}{2\left(x^2+2\right)}\)
\(=-\frac{1}{2}+\frac{x^2+4x+4}{2\left(x^2+2\right)}=-\frac{1}{2}+\frac{\left(x+2\right)^2}{2\left(x^2+2\right)}\ge-\frac{1}{2}\)
Dấu "=" xảy ra \(\Leftrightarrow\frac{\left(x+2\right)^2}{2\left(x^2+2\right)}=0\Leftrightarrow x+2=0\Leftrightarrow x=-2\)
Vậy GTNN của biểu thức là \(-\frac{1}{2}\) tại \(x=-2\)
1 tháng 6 2017
A=(1/x-2 - (2x/(2-x)(2+x) - 1/2+x) ) *(2-x)/x
=(1/x-2 - x^2+5x-2/(2-x)(2+x))*2-x/x
=(-x^3-4x^2+12x/(x-2)(2-x)(2+x))*2-x/x
= - x(x-2)(x+6)(2-x)/x(x-2)(2-x)(2+x)
= - x+6/x+2
12 tháng 2 2020
a) ĐKXĐ: x≠-5
Ta có: \(\frac{2x-5}{x+5}=3\)
\(\Leftrightarrow\frac{2x-5}{x+5}-3=0\)
\(\Leftrightarrow\frac{2x-5}{x+5}-\frac{3\left(x+5\right)}{x+5}=0\)
\(\Leftrightarrow2x-5-3\left(x+5\right)=0\)
\(\Leftrightarrow2x-5-3x-15=0\)
\(\Leftrightarrow-x-20=0\)
\(\Leftrightarrow-x=20\)
\(\Leftrightarrow x=-20\)(tmđk)
Vậy: x=-20
b) ĐKXĐ: x≠1;x≠-1
Ta có: \(\frac{2}{x-1}=\frac{6}{x+1}\)
\(\Leftrightarrow\frac{2}{x-1}-\frac{6}{x+1}=0\)
\(\Leftrightarrow\frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{6\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=0\)
\(\Leftrightarrow2\left(x+1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow2x+2-6x+6=0\)
\(\Leftrightarrow-4x+8=0\)
\(\Leftrightarrow-4x=-8\)
\(\Leftrightarrow x=2\)(tmđk)
Vậy: x=2
c) ĐKXĐ: x≠1;x≠-1
Ta có: \(\frac{2x+1}{x-1}=\frac{5\left(x-1\right)}{x+1}\)
\(\Leftrightarrow\frac{2x+1}{x-1}-\frac{5\left(x-1\right)}{x+1}=0\)
\(\Leftrightarrow\frac{\left(2x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{5\left(x-1\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=0\)
\(\Leftrightarrow\left(2x+1\right)\left(x+1\right)-5\left(x^2-2x+1\right)=0\)
\(\Leftrightarrow2x^2+2x+x+1-5x^2+10x-5=0\)
\(\Leftrightarrow-3x^2+13x-4=0\)
\(\Leftrightarrow-3x^2+x+12x-4=0\)
\(\Leftrightarrow x\left(-3x+1\right)+4\left(3x-1\right)=0\)
\(\Leftrightarrow x\left(1-3x\right)-4\left(1-3x\right)=0\)
\(\Leftrightarrow\left(1-3x\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}1-3x=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=1\\x=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{3}\\x=4\end{matrix}\right.\)(thỏa mãn điều kiện)
Vậy: \(x\in\left\{\frac{1}{3};4\right\}\)
d) ĐKXĐ: x≠1;x≠-1
Ta có: \(\frac{x}{x-1}-\frac{2x}{x^2-1}=0\)
\(\Leftrightarrow\frac{x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{2x}{\left(x-1\right)\left(x+1\right)}=0\)
\(\Leftrightarrow x\left(x+1\right)-2x=0\)
\(\Leftrightarrow x^2+x-2x=0\)
\(\Leftrightarrow x^2-x=0\)
\(\Leftrightarrow x\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=1\left(ktm\right)\end{matrix}\right.\)
Vậy: x=0
e) ĐKXĐ: x≠2
Ta có: \(\frac{1}{x-2}+3=\frac{x-3}{2-x}\)
⇔\(\frac{1}{x-2}+3-\frac{x-3}{2-x}=0\)
⇔\(\frac{1}{x-2}+3+\frac{x-3}{x-2}=0\)
⇔\(\frac{1}{x-2}+\frac{3\left(x-2\right)}{x-2}+\frac{x-3}{x-2}=0\)
\(\Leftrightarrow1+3\left(x-2\right)+x-3=0\)
\(\Leftrightarrow1+3x-6+x-3=0\)
\(\Leftrightarrow4x-8=0\)
\(\Leftrightarrow4x=8\)
\(\Leftrightarrow x=2\)(không thỏa mãn)
Vậy: x∈∅
f) ĐKXĐ: \(x\ne\pm2\)
Ta có: \(\frac{x+1}{x-2}+\frac{x-1}{x+2}=\frac{2\left(x^2+2\right)}{x^2-4}\)
⇔\(\frac{x+1}{x-2}+\frac{x-1}{x+2}-\frac{2\left(x^2+2\right)}{x^2-4}=0\)
⇔\(\frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{\left(x-1\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\frac{2x^2+4}{\left(x+2\right)\left(x-2\right)}=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+2\right)+\left(x-1\right)\left(x-2\right)-2x^2-4=0\)
\(\Leftrightarrow x^2+2x+x+2+x^2-2x-x+2-2x^2-4=0\)
\(\Leftrightarrow0=0\)
Vậy: x∈R
g) ĐKXĐ: \(x\ne\pm2\)
Ta có: \(\frac{x+2}{x-2}+\frac{1}{x+2}=\frac{x\left(x-5\right)}{x^2-4}\)
⇔\(\frac{x+2}{x-2}+\frac{1}{x+2}-\frac{x\left(x-5\right)}{\left(x-2\right)\left(x+2\right)}=0\)
⇔\(\frac{\left(x+2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{\left(x+2\right)\left(x-2\right)}-\frac{x^2-5x}{\left(x-2\right)\left(x+2\right)}=0\)
⇔\(\left(x+2\right)^2+x-2-x^2+5x=0\)
\(\Leftrightarrow x^2+4x+4+x-2-x^2+5x=0\)
\(\Leftrightarrow10x-2=0\)
\(\Leftrightarrow10x=2\)
\(\Leftrightarrow x=\frac{2}{10}=\frac{1}{5}\)(thỏa mãn)
Vậy: \(x=\frac{1}{5}\)