xU 36 và 6 36
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21 tháng 2 2017
Ta có: \(\frac{36}{x+6}+\frac{36}{x-6}=\frac{9}{2}\)
ĐKXĐ: \(\left\{\begin{matrix}x\ne-6\\x\ne6\end{matrix}\right.\)
\(\Leftrightarrow36\left(\frac{1}{x+6}+\frac{1}{x-6}\right)=\frac{9}{2}\)
\(\Leftrightarrow36\left(\frac{x-6+x+6}{\left(x+6\right)\left(x-6\right)}\right)=\frac{9}{2}\)
\(\Leftrightarrow36.\frac{2x}{x^2-36}=\frac{9}{2}\)
\(\Leftrightarrow\frac{72x}{x^2-36}=\frac{9}{2}\)
\(\Leftrightarrow72x.2=9.\left(x^2-36\right)\)
\(\Leftrightarrow8x.2=x^2-36\) ( chia cả hai vế cho 9 )
\(\Leftrightarrow16x=x^2-36\)
\(\Leftrightarrow16x-x^2+36=0\)
\(\Leftrightarrow-x^2+16x+36=0\)
\(\Leftrightarrow x^2-16x-36=0\)
\(\Leftrightarrow x^2+2x-18x-36=0\)
\(\Leftrightarrow x\left(x+2\right)-18\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x-18\right)=0\)
\(\Leftrightarrow\left[\begin{matrix}x+2=0\\x-18=0\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=-2\\x=18\end{matrix}\right.\)
Vậy: \(x=-2;18\)
21 tháng 2 2017
\(\frac{36}{x+6}+\frac{36}{x-6}=4,5\left(đkxđ:x\ne\pm6\right)\)
\(\Leftrightarrow\frac{36\left(x-6\right)+36\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}=\frac{4,5\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}\)
\(\Leftrightarrow\frac{36\left(x-6+x+6\right)}{\left(x-6\right)\left(x+6\right)}=\frac{4,5\left(x^2-36\right)}{\left(x-6\right)\left(x+6\right)}\)
\(\Rightarrow36\times2x=4,5\left(x^2-36\right)\)
\(\Leftrightarrow72x=4,5x^2-162\)
\(\Leftrightarrow4,5x^2-72x-162=0\)
\(\Leftrightarrow4,5x^2+9x-81x-162=0\)
\(\Leftrightarrow4,5x\left(x+2\right)-81\left(x+2\right)=0\)
\(\Leftrightarrow\left(4,5x-81\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[\begin{matrix}4,5x-81=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=18\\x=-2\end{matrix}\right.\left(TMĐKXĐ\right)\)
HD
0
IA
10 tháng 3 2020
Trả lời:
-36 < x < 36 => x thuộc { -36 ; -35 ; -34 ; ...... ; -2 ; -1 ; 0 ; 1 ; 2; ...... ; 34 ; 35 ; 36 }
Mà x thuộc B ( 6 ) => x thuộc { -36 ; -24 ; -18 ; -12 ; -6 ; 6 ; 12 ; 18 ; 24 ; 30 ; 36 }
[cry] [cry] [cry] [cry] [cry] [cry]
K
2
23 tháng 2 2022
\(\Leftrightarrow36\left(x+6\right)+36\left(x-6\right)=\dfrac{9}{2}\left(x^2-36\right)\)
\(\Leftrightarrow x^2\cdot\dfrac{9}{2}-162-72x=0\)
\(\Leftrightarrow9x^2-144x-324=0\)
\(\Leftrightarrow x^2-16x-36=0\)
=>(x-18)(x+2)=0
=>x=18 hoặc x=-2
23 tháng 2 2022
ĐKXĐ:\(x\ne\pm6\)
\(\dfrac{36}{x-6}+\dfrac{36}{x+6}=4,5\\ \Leftrightarrow36\left(\dfrac{1}{x-6}+\dfrac{1}{x+6}\right)=4,5\\ \Leftrightarrow\dfrac{x+6}{\left(x-6\right)\left(x+6\right)}+\dfrac{x-6}{\left(x-6\right)\left(x+6\right)}=\dfrac{1}{8}\\ \Leftrightarrow\dfrac{x+6+x-6}{x^2-36}=\dfrac{1}{8}\\ \Leftrightarrow\dfrac{2x}{x^2-36}=\dfrac{1}{8}\\ \Leftrightarrow x^2-36=16x\\ \Leftrightarrow x^2-16x-36=0\\ \Leftrightarrow\left(x^2+2x\right)-\left(18x+36\right)=0\\ \Leftrightarrow x\left(x+2\right)-18\left(x+2\right)=0\\ \Leftrightarrow\left(x+2\right)\left(x-18\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\left(tm\right)\\x=18\left(tm\right)\end{matrix}\right.\)
PT
1
30 tháng 4 2021
\(\dfrac{36}{x+6}+\dfrac{36}{x-6}=4,5\)
\(\Leftrightarrow36\left(x-6\right)+36\left(x+6\right)=4,5\left(x^2-36\right)\)
\(\Leftrightarrow36x-216+36x+216=4,5x^2-162\)
\(\Leftrightarrow-4,5x^2+72x+162=0\)
\(\Leftrightarrow\left(x-18\right)\left(-4,5x-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=18\\x=-2\end{matrix}\right.\)
1 tháng 5 2021
bạn làm rõ hơn ở chỗ này đc ko, mk ko hiểu
⇔−4,5x2+72x+162=0⇔−4,5x2+72x+162=0
⇔(x−18)(−4,5x−9)=0
NV
2