tìm x:
6,5 - 9/4 : |x+1/3| = 2
giúp mình vs ạ
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\(\dfrac{1}{x-1}+1=\dfrac{x}{x-2}\\ \Rightarrow\dfrac{1+x-1}{x-1}=\dfrac{x}{x-2}\\ \dfrac{x}{x-1}=\dfrac{x}{x-2}\\ \Leftrightarrow x\left(x-2\right)=x\left(x-1\right)\\ x^2-2x=x^2-x\\ x^2-x^2=x-2x\\ -x=0\\ x=0\)
\(\Leftrightarrow x+2+x^2-3x+2=x^2-x\)
=>-2x+4+x=0
=>4-x=0
hay x=4
\(\dfrac{3}{x-5}=\dfrac{-4}{x+2}\left(x\ne5;-2\right).\\ \Leftrightarrow\dfrac{3}{x-5}+\dfrac{4}{x+2}=0.\\ \Leftrightarrow\dfrac{3x+6+4x-20}{\left(x-5\right)\left(x+2\right)}=0.\\ \Rightarrow7x=14.\\ \Leftrightarrow x=2\left(TM\right).\)
x+1<x+2<x+3<x+4 ( với mọi x)
\(\dfrac{1}{100}\) < \(\dfrac{1}{99}\)<\(\dfrac{1}{3}\) <\(\dfrac{1}{2}\)
=>\(\dfrac{x+1}{100}\)+\(\dfrac{x+2}{99}\) <\(\dfrac{x+3}{3}\)+\(\dfrac{x+4}{2}\) là đúng
\(|-2x+1,5|=\dfrac{1}{4}\Rightarrow-2x+1,5=\pm\dfrac{1}{4}\)
\(-2x+1,5=\dfrac{1}{4}\Rightarrow-2x=1,5-0,25\Rightarrow-2x=1,25\Rightarrow x=1,25:\left(-2\right)\Rightarrow x=...\)
\(-2x+1,5=-\dfrac{1}{4}\Rightarrow-2x=-0,25-1,5\Rightarrow-2x=1,75\Rightarrow x=1,75:\left(-2\right)\Rightarrow x=...\)
\(\dfrac{3}{2}-|1.\dfrac{1}{4}+3x|=\dfrac{1}{4}\Rightarrow|1.\dfrac{1}{4}+3x|=\dfrac{3}{2}-\dfrac{1}{4}\Rightarrow|1.\dfrac{1}{4}+3x|=\dfrac{5}{4}\)
\(\Rightarrow1.\dfrac{1}{4}+3x=\pm\dfrac{5}{4}\)
\(1.\dfrac{1}{4}+3x=\dfrac{5}{4}\Rightarrow\dfrac{1}{4}+3x=\dfrac{5}{4}\Rightarrow3x=\dfrac{5}{4}-\dfrac{1}{4}\Rightarrow3x=1\Rightarrow x=3\)
\(1.\dfrac{1}{4}+3x=-\dfrac{5}{4}\Rightarrow\dfrac{1}{4}+3x=-\dfrac{5}{4}\Rightarrow3x=-\dfrac{5}{4}-\dfrac{1}{4}\Rightarrow3x=-\dfrac{3}{2}x=...\)
\(2^{x+1}-2^x=3^2\)
\(\Rightarrow2^x\cdot\left(2-1\right)=9\)
\(\Rightarrow2^x=9\)
\(\Rightarrow x\in\varnothing\)
\(2^{x+1}-2^x=3^2\)
=>2^x*2-2^x=9
=>2^x=9
=>\(x\in\varnothing\)
Đặt \(x+2=t\ne0\Rightarrow x+1=t-1\)
\(A=\dfrac{x+1}{\left(x+2\right)^2}=\dfrac{t-1}{t^2}=-\dfrac{1}{t^2}+\dfrac{1}{t}=-\left(\dfrac{1}{t}-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\le\dfrac{1}{4}\)
\(A_{max}=\dfrac{1}{4}\) khi \(t=2\) hay \(x=0\)
x=13/42 hoặc -41/42