Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\left|2x-1\right|=\dfrac{3}{2}\\ \Rightarrow\left[{}\begin{matrix}2x-1=\dfrac{3}{2}\\2x-1=-\dfrac{3}{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)
Thay \(x=\dfrac{5}{4}\) vào D ta có:
\(D=4x+3=4.\dfrac{5}{4}+3=5+3=8\)
Thay \(x=-\dfrac{1}{4}\) vào D ta có:
\(D=4.\dfrac{-1}{4}+3=-1+3=2\)
Để \(D=\dfrac{3}{2}\)
\(\Leftrightarrow4x+3=\dfrac{3}{2}\\ \Leftrightarrow4x=-\dfrac{3}{2}\\ \Leftrightarrow x=-\dfrac{3}{8}\)
Xét \(\left(a+b+c\right)\left(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{c+a}\right)=126.16=2016\)
\(\Leftrightarrow1+\dfrac{c}{a+b}+1+\dfrac{a}{b+c}+1+\dfrac{b}{c+a}=2016\)
\(\Leftrightarrow\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}=2013\)
Vậy A = 2013
\(A=\left|\dfrac{3}{5}-x\right|+\dfrac{1}{9}\ge\dfrac{1}{9}\\ A_{min}=\dfrac{1}{9}\Leftrightarrow x=\dfrac{3}{5}\\ B=\dfrac{2009}{2008}-\left|x-\dfrac{3}{5}\right|\le\dfrac{2009}{2008}\\ B_{max}=\dfrac{2009}{2008}\Leftrightarrow x=\dfrac{3}{5}\\ C=-2\left|\dfrac{1}{3}x+4\right|+1\dfrac{2}{3}\le1\dfrac{2}{3}\\ C_{max}=1\dfrac{2}{3}\Leftrightarrow\dfrac{1}{3}x=-4\Leftrightarrow x=-12\)
a: \(\left|a-2b+3\right|^{2023}>=0\forall a,b\)
\(\left(b-1\right)^{2024}>=0\forall b\)
Do đó: \(\left|a-2b+3\right|^{2023}+\left(b-1\right)^{2024}>=0\forall a,b\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}a-2b+3=0\\b-1=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}b=1\\a=2b-3=2\cdot1-3=-1\end{matrix}\right.\)
Thay a=-1 và b=1 vào P, ta được:
\(P=\left(-1\right)^{2023}\cdot1^{2024}+2024=2024-1=2023\)
\(\left|x-\dfrac{1}{2}\right|-1=\dfrac{5}{2}\)
\(\Rightarrow\left|x-\dfrac{1}{2}\right|=\dfrac{5}{2}+1\)
\(\Rightarrow\left|x-\dfrac{1}{2}\right|=\dfrac{7}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{7}{2}\\x-\dfrac{1}{2}=-\dfrac{7}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)