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Bài 2:
a: =>x=0 hoặc x=-3
b: =>x-2=0 hoặc 5-x=0
=>x=2 hoặc x=5
c: =>x-1=0
hay x=1
\(a,\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{5}=0\\\dfrac{8}{5}+2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{5}\\x=\dfrac{4}{5}\end{matrix}\right.\)
\(b,\dfrac{x-\dfrac{4}{7}}{x+\dfrac{1}{2}}>0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-\dfrac{4}{7}>0\\x+\dfrac{1}{2}>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-\dfrac{4}{7}< 0\\x+\dfrac{1}{2}< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{4}{7}\\x< -\dfrac{1}{2}\end{matrix}\right.\)
\(c,\dfrac{2x-3}{x+\dfrac{7}{4}}< 0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-3< 0\\x+\dfrac{7}{4}>0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-3>0\\x+\dfrac{7}{4}< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< \dfrac{3}{2}\\x >-\dfrac{7}{4}\end{matrix}\right.\\\left\{{}\begin{matrix}x>\dfrac{3}{2}\\x< -\dfrac{7}{4}\end{matrix}\right.\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}-\dfrac{7}{4}< x< \dfrac{3}{2}\\x\in\varnothing\end{matrix}\right.\Leftrightarrow-\dfrac{7}{4}< x< \dfrac{3}{2}\)
\(a,A=\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)-2018\)
\(=\left(x^2+5x-6\right)\left(x^2+5x+6\right)-2018\)
Đặt \(x^2+5x=a\)
\(\Rightarrow A=\left(a-6\right)\left(a+6\right)-2018=a^2-2054\)
\(\Rightarrow A_{min}=2054\Leftrightarrow a=0\)
\(\Rightarrow x^2+5x=0\Leftrightarrow x\left(x+5\right)=0\)
\(\Leftrightarrow x\in\left\{0;-5\right\}\)
\(b,B=\left(x-1\right)\left(x-4\right)\left(x-5\right)\left(x-8\right)+2018.\)
\(=\left(x^2-9x+8\right)\left(x^2-9x+20\right)+2018\)
Đặt \(x^2-9x+14=a\)
\(\Rightarrow B=\left(a-6\right)\left(a+6\right)+2018\)
\(=a^2-36+2018=a^2+1982\)
\(\Rightarrow B_{min}=1982\Leftrightarrow a^2=0\Rightarrow a=0\)
\(\Rightarrow x^2-9x+14=0\)
\(\Rightarrow x^2-2x-7x+14=0\)
\(\Leftrightarrow x\left(x-2\right)-7\left(x-2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x-7\right)=0\)
\(\Rightarrow x\in\left\{2;7\right\}\)
a) \(\frac{x+2015}{5}+\frac{x+2015}{6}=\frac{x+2015}{7}+\frac{x+2015}{8}\)
\(\frac{x+2015}{5}+\frac{x+2015}{6}-\frac{x+2015}{7}-\frac{x+2015}{8}=0\)
\(\left(x+2015\right).\left(\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}\right)=0\)
vì \(\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}\ne0\)
\(\Rightarrow\)x + 2015 = 0
\(\Rightarrow\)x = -2015
b) Tương tự
a)(x-2016)^x.(x-2016)-(x-2015)^x.(x-2015)^10=0
mik chỉ làm đc đến đây thôi mk lớp 6 :)
