x+1/x-1+x-2/x+2+x-3/x+3+x+4/x-4=0
help me
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`(3x+2)*(x+4)-(3x-1)*(x-5)=0`
\(\Leftrightarrow3x\left(x+4\right)+2\left(x+4\right)-3x\left(x-5\right)+1\left(x-5\right)=0\)
\(\Leftrightarrow3x^2+3x\cdot4+2x+2\cdot4-3x^2+3x\cdot5+x-5=0\)
\(\Leftrightarrow3x^2+12x+2x+8-3x^2+15x+x-5=0\)
\(\Leftrightarrow\left(3x^2-3x^2\right)+\left(12x+2x+15x+x\right)+\left(8-5\right)=0\)
\(\Leftrightarrow30x+3=0\)
\(\Leftrightarrow30x=0-3\)
`=> 30x=-3`
`-> x=-3 \div 30`
`-> x=-1/10 `
\(DKXD:x\ne\sqrt[3]{4}\approx1,58\in\left(-2;2\right)\)
Vậy thì hàm sẽ gián đoạn trên khoảng \(\left(-2;2\right)\) => đáp án A sai, còn lại tất cả đều đúng
Nguyễn Trà My
Phần a)
\(3\times\left(\frac{1}{2}-x\right)+\frac{1}{3}=\frac{7}{6}-x\)
\(32-3x+13=76-x\)
\(116-3x=76-x\)
\(116-76=3x-x\)
\(46=2x\)
\(x=46\div2\)
\(x=13\)
a: =>2x>-6
hay x>-3
e: =>(5-x)/x<0
=>0<x<5
h: \(\Leftrightarrow\dfrac{x+5-x-3}{x+3}< 0\)
\(\Leftrightarrow x+3< 0\)
hay x<-3
g: \(\Leftrightarrow\dfrac{2x+7}{x+4}>0\)
\(\Leftrightarrow\left[{}\begin{matrix}x>-\dfrac{7}{2}\\x< -4\end{matrix}\right.\)
Vậy xét là \(\frac{1}{2}+1\)nhé.
a,\(\frac{3}{2}x\frac{4}{3}x\frac{5}{4}x...x\frac{1000}{999}\)
=3x4x5x...x1000/2x3x4x...x999
=1000/2=500
b, c tương tự câu a
)(1/2+1)x(1/3+1)x(1/4+1)x...x(1/999+1)
b)(1/2-1)x(1/3-1)x(1/4-1)x...x(1/1000-1)
c)3/22 x 8/32 x 15/42 x .... x 99/102
mình ko biết làm chép lại de thui
a) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)=\left(x^2-1\right)\left[\left(x^2-1\right)^2-\left(x^4+x^2+1\right)\right]\)
\(=\left(x^2-1\right)\left(x^4-2x^2+1-x^4-x^2-1\right)=\left(x^2-1\right)\left(-3x^2\right)\)
\(=-3x^4+3x^2=3\left(x^2-x^4\right)=3\left(x-x^2\right)\left(x+x^2\right)=\left(3x-3x^2\right)\left(x+x^2\right).\)
b)\(\left(x^4-3x^2+9\right)\left(x^2+3-\left(3+x^2\right)\right)^3=\left(x^4-3x^2+9\right).0^3=0\)
c)\(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2=\left(x-3\right)^3-\left(x^3-3^3\right)+6\left(x^2+2x+1\right)\)
\(=\left(x-3\right)^3-\left[\left(x-3\right)^3+3.x.3.\left(x-3\right)\right]+6x^2+12x+6\)
\(=6x^2+12x+6-9x\left(x-3\right)=6x^2+12x+6-9x^2+27x\)
\(=39x-3x^2+6=3\left(13x-x^2+2\right).\)
\(\dfrac{x+1}{x-1}+\dfrac{x-2}{x+2}+\dfrac{x-3}{x+3}+\dfrac{x+4}{x-4}=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x-4\right)+\left(x-2\right)\left(x-1\right)\left(x+3\right)\left(x-4\right)+\left(x-3\right)\left(x-1\right)\left(x+2\right)\left(x-4\right)+\left(x+4\right)\left(x-1\right)\left(x+2\right)\left(x+3\right)=0\)
\(\Leftrightarrow4x^4+20x-96=0\)
\(\Leftrightarrow4\left(x^4+5x-24\right)=0\)
\(\Leftrightarrow x^4+5x-24=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2,45...\\x=1,94...\end{matrix}\right.\)
Vậy: \(S=\left\{-2,45...;1,94...\right\}\)
còn cách khác ko bn