tìm x biết
3,8 : (2x) = 1/4 : 2+2/3
giúp mình ....cảm ơn
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Bài 1:
a) \(x\left(x+1\right)+x\left(x-1\right)-2x^2\)
\(=x^2+x+x^2-x-2x^2\)
\(=2x^2-2x^2\)
\(=0\)
b) \(\left(x+2\right)\left(x^2-x+1\right)-\left(x-2\right)\left(x^2+x+1\right)\)
\(=x^3-x^2+x+2x^2-2x+2-x^3-x^2-x+2x^2+2x+2\)
\(=\left(x^3-x^3\right)+\left(-x^2+2x^2-x^2+2x^2\right)+\left(x-2x-x+2x\right)+\left(2+2\right)\)
\(=2x^2+4\)
c) \(\left(3-x\right)^2+2\left(x-3\right)\left(x+7\right)+\left(x+7\right)^2\)
\(=\left(x-3\right)^2+2\left(x-3\right)\left(x+7\right)+\left(x+7\right)^2\)
\(=\left[\left(x-3\right)+\left(x+7\right)\right]^2\)
\(=\left(x-3+x+7\right)^2\)
\(=\left(2x+4\right)^2\)
\(=-7\cdot\left[16+\left(-36\right):\left(-9\right)\right]+125=-77\cdot20+125=-140+125=-15\)
b: \(=\dfrac{3a-9-2a-6-6}{\left(a+3\right)\left(a-3\right)}=\dfrac{a-15}{a^2-9}\)
\(\dfrac{-2}{3}\left(x-\dfrac{1}{4}\right)=\dfrac{1}{3}\left(2x-1\right)\)
\(\Leftrightarrow\dfrac{-2}{3}x+\dfrac{1}{6}=\dfrac{2}{3}x-\dfrac{1}{3}\)
\(\Leftrightarrow\dfrac{-2}{3}x-\dfrac{2}{3}x=\dfrac{-1}{3}-\dfrac{1}{6}\)
\(\Leftrightarrow\dfrac{-4}{3}x=\dfrac{-1}{2}\)
\(\Leftrightarrow x=\dfrac{3}{8}\)
Vậy \(x=\dfrac{3}{8}\)
\(\left(x^2+1\right)\left(x-2\right)+2x=4\Leftrightarrow x^3-2x^2+x-2+2x-4=0\Leftrightarrow x^3-2x^2+3x-6=0\Leftrightarrow\left(x-2\right)\left(x^2+3\right)=0\Leftrightarrow x-2=0\Leftrightarrow x=2\)(do \(x^2+3\ge3>0\))
Câu 1:
\(4x^2+16x-9\)
\(=4x^2+18x-2x-9\)
\(=2x\left(2x+9\right)-\left(2x+9\right)\)
\(=\left(2x-1\right)\left(2x+9\right)\)
Câu 2:
\(6x^2-11x+3=0\)
\(\Leftrightarrow6x^2-2x-9x+3=0\)
\(\Leftrightarrow2x\left(3x-1\right)-3\left(3x-1\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(3x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=3\\3x=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)
\(2x^4-x^3+2x^2+1=2x^4-2x^3+2x^2+x^3-x^2+x+x^2-x+1\\ \)
\(=2x^2\left(x^2-x+1\right)+x\left(x^2-x+1\right)+\left(x^2-x+1\right)=\left(x^2-x+1\right)\left(2x^2+x+1\right)\)
Vậy a = 2; b = 1; c = 1.
\(a,\left|2x+\dfrac{1}{2}\right|=0\\ \Leftrightarrow2x+\dfrac{1}{2}=0\\ \Leftrightarrow2x=-\dfrac{1}{2}\\ \Leftrightarrow x=-\dfrac{1}{4}\\ b,\left|3x+\dfrac{3}{4}\right|=3\\ \Leftrightarrow\left[{}\begin{matrix}3x+\dfrac{3}{4}=3\\3x+\dfrac{3}{4}=-3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}3x=\dfrac{9}{4}\\3x=-\dfrac{15}{4}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=-\dfrac{5}{4}\end{matrix}\right.\)
3,8 : 2x = 1/4 : 2 + 2/3
3,8 : 2x = 19/24
2x = 24/5
x = 12/5