tim x biết 1/x - 1/x+1=1/2
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\(3\left(5x-1\right)-x\left(x+1\right)+x^2=14\)
\(\Leftrightarrow15x-3-x^2-x+x^2=14\)
\(\Leftrightarrow\left(x^2-x^2\right)+\left(15x-x\right)-3=14\)
\(\Leftrightarrow14x=17\)
\(\Leftrightarrow x=\frac{17}{14}\)
Vậy \(x=\frac{17}{14}\)
3(5x - 1) - x(x+1)+x 2 = 14
➡️15x - 3 - x 2 - x + x 2 = 14
➡️(15x - x ) + ( -x 2 + x 2 ) - 3= 14
➡️14x -3 = 14
➡️14x = 14+3
➡️14x = 17
➡️x = 17/14
Hok tốt~
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1) \(M=\frac{x^2+y^2+7}{x^2+y^2+5}=1+\frac{2}{x^2+y^2+5}\)
Ta có: \(x^2+y^2\ge0,\forall x;y\)
=> \(x^2+y^2+5\ge5\) với mọi x; y
=> \(\frac{2}{x^2+y^2+5}\le\frac{2}{5}\)
=> \(M\le1+\frac{2}{5}=\frac{7}{5}\)
Dấu "=" xảy ra <=> x = y = 0
Vậy max M = 7/5 đạt tại x = y = 0
2) \(f\left(x-1\right)=x^2-3x+5=x^2-x-2x+2+3\)
\(=x\left(x-1\right)-2\left(x-1\right)+3=x\left(x-1\right)-\left(x-1\right)-\left(x-1\right)+3\)
\(=\left(x-1\right)\left(x-1\right)-\left(x-1\right)+3\)
=> \(f\left(x\right)=x.x-x+3=x^2-x+3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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x + (x + 1) + (x + 2) + ... + (x + 2003) = 2004
=> x + x + 1 + x + 2 + .... + x + 2003 = 2004
=> 2004x + 2007006 = 2004
=> 2004x = 2005002
=> x = 1000,5
Ta có: \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+2003\right)=2004\)
\(\Leftrightarrow2004x+2007006=2004\)
\(\Leftrightarrow2004x=-2005002\)
hay \(x=-\dfrac{2001}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Mình làm theo ý hiểu, chứ cái đề chả rõ ràng gì.
\(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Leftrightarrow\left(x+1\right)^2=8.2\)
\(\Leftrightarrow\left(x+1\right)^2=16\)
\(\Leftrightarrow\left(x+1\right)^2=4^2\)hay \(\left(x+1\right)^2=\left(-4\right)^2\)
\(\Leftrightarrow x+1=4\)hay \(x+1=-4\)
\(\Leftrightarrow x=3\)hay \(x=-5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3x+4=0\Leftrightarrow x=-\dfrac{4}{3}\\ 2x\left(x-1\right)-\left(1+2x\right)=-34\\ \Leftrightarrow2x^2-2x-1-2x=-34\\ \Leftrightarrow2x^2-4x+33=0\\ \Leftrightarrow2\left(x^2-2x+1\right)+30=0\\ \Leftrightarrow2\left(x-1\right)^2+30=0\\ \Leftrightarrow x\in\varnothing\left[2\left(x-1\right)^2+30\ge30>0\right]\\ x^2+9x-10=0\\ \Leftrightarrow x^2-x+10x-10=0\\ \Leftrightarrow\left(x-1\right)\left(x+10\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-10\end{matrix}\right.\\ \left(7x-1\right)\left(2+5x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}7x-1=0\\2+5x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{7}\\x=-\dfrac{2}{5}\end{matrix}\right.\)
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(+) Th1: l x - 1 l = x - 1 khi x - 1 >= 0 => x >= 1
Thay vào pt ta có:
x - 1 = x + 2
0x = 3 ( loại )
(+) Th2 : l x - 1 l = 1 - x khi x - 1 <=0 => x <= 1
Thay vào ta có :
1 - x = x + 2
-x - x = 2 - 1
-2x = 1
x = -1/2 ( Tm)
Vậy x = -1/2
x=1
chắc chắn lun đó. cho 1 like nha
Ta có:
\(\frac{1}{x}-\frac{1}{x+1}=\frac{1}{2}\)
\(\frac{x+1}{x.\left(x+1\right)}-\frac{x}{x.\left(x+1\right)}=\frac{1}{2}\)
\(\frac{x+1-x}{x.\left(x+1\right)}=\frac{1}{2}\)
\(\frac{1}{x.\left(x+1\right)}=\frac{1}{1.2}\)
\(x.\left(x+1\right)=1.2\)
Vì x và x+1 là 2 số tự nhiên liên tiếp mà x<x+1
=>x=1, x+1=2
Vậy x=1