Giúp mình vs: (x-1)^x+2=(x-1)^x-6 cảm ơn nh nha
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\(\dfrac{3-3x}{\left(1+x\right)^2}:\dfrac{6x^2-6}{x+1}\)
\(=\dfrac{3\left(1-x\right)}{\left(x+1\right)^2}:\dfrac{6\left(x^2-1\right)}{x+1}\)
\(=\dfrac{-3\left(x-1\right)}{\left(x+1\right)^2}:\dfrac{6\left(x+1\right)\left(x-1\right)}{x+1}\)
\(=\dfrac{-3\left(x-1\right)}{\left(x+1\right)^2}\cdot\dfrac{x+1}{6\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{-3\left(x-1\right)\left(x+1\right)}{6\left(x+1\right)^3\left(x-1\right)}=\dfrac{-3\left(x+1\right)}{6\left(x+1\right)\left(x+1\right)^2}=\dfrac{-3}{6\left(x+1\right)^2}=\dfrac{-1}{2\left(x+1\right)^2}\)
b) Bạn có thể viết kiểu latex được không ạ ?
\(\left(x+2\right)\left(\dfrac{360}{x}-6\right)=360\)
\(ĐK:x\ne0\)
\(\Leftrightarrow\left(x+2\right)\left(\dfrac{360-6x}{x}\right)=360\)
\(\Leftrightarrow360-6x+\dfrac{720-12x}{x}=360\)
\(\Leftrightarrow360x-6x^2+720-12x=360x\)
\(\Leftrightarrow6x^2+12x-720=0\)
\(\Delta=12^2-4.6.\left(-720\right)\)
\(=17424>0\)
`->` pt có 2 nghiệm
\(\left\{{}\begin{matrix}x_1=\dfrac{-12-\sqrt{17424}}{12}=-12\\x_2=\dfrac{-12+\sqrt{17424}}{12}=10\end{matrix}\right.\) ( tm )
Vậy \(S=\left\{-12;10\right\}\)
\(\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right):2}=\frac{2009}{2011}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2009}{2011}\)
\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{2011}:2\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{4022}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2009}{4022}\)
\(\frac{1}{x+1}=\frac{1}{2011}\)
=>x+1=2011
=>x=2010
Dùng công thức tính tổng
\(1+2+3+...+x=11325\)
\(\Leftrightarrow\frac{x\left(x+1\right)}{2}=11325\)
\(\Leftrightarrow x\left(x+1\right)=22650\)
\(\Leftrightarrow x\left(x+1\right)=150.151\)
Nên x = 150
Vậy ,,,
\(1+2+3+4+...+x=11325\)
\(\Rightarrow\frac{x\left(x+1\right)}{2}=11325\)
\(\Rightarrow x\left(x+1\right)=11325\times2\)
\(\Rightarrow x\left(x+1\right)=22650\)
\(\Rightarrow150\times151=22650\)
\(\Rightarrow x=150\)
1.
2|x-6|+7x-2=|x-6|+7x
2|x-6| - |x-6|=7x-(7x-2)
|x-6| = 2
=>x-6 = +2
*x-6=2 *x-6 = -2
x =2+6 x = (-2)+6
x =8 x = 4
2.
|x-5|-7(x+4)=5-7x
|x-5|-7x-28 =5-7x
|x-5|-28 =5-7x+7x
|x-5|-28 = 5
|x-5| = 5+28
|x-5| = 33
=>x-5 = +33
*x-5=33 *x-5=-33
x =38 x = -28
3.
3|x+4|-2(x-1)=7-2x
3|x+4|-2x+2 =7-2x
3|x+4|-2 =7-2x+2x
3|x+4|-2 =7
3|x+4| =7+2
3|x+4| = 9
|x+4| =9:3
|x+4| = 3
=>x+4 = +3
*x+4=3 *x+4=-3
x =-1 x = -7
(x-1)x+2 = (x-1)x-6
<=> (x-1)x-6 + (x-1)x+2 =0
<=> (x-1)x+2 . (x-1)-8 +(x-1)x+2 =0
<=> (x-1)x+2 . [ (x-1)-8 +1 ] =0
<=> (x-1)x+2 =0 hoặc (x-1)-8 +1 =0
<=> x-1 =0 hoặc (x-1)-8 =-1
<=> x=0+1=1 hoặc (x-1) =-1
<=> x=1 hoặc x=0
Vậy x=1 hoặc x=0
Tích mk nha pn....Pn nào thấy đúng tích + kb, theo dõi mk nha....