Áp dụng BĐT giá trị tuyệt đối:
\(\left|x-1\right|+\left|x-5\right|=\left|x-1\right|+\left|5-x\right|\ge\left|x-1+5-x\right|=\left|4\right|=4\)
Dấu "=" xảy ra khi \(\left(x-1\right)\left(5-x\right)\ge0\)
\(\Rightarrow x-1,5-x\) cùng dấu
Nếu \(x-1,5-x\ge0\) thì \(x\ge1;5\ge x\Leftrightarrow1\le x\le5\)
Nếu \(x-1,5-x\le0\) thì \(x\le1;x\ge5\)(loại)
CMR :
a, \(\left|x-1\right|+\left|x-3\right|+\left|x-5\right|+\left|x-7\right|\ge8\)
b, \(\left|x+1\right|+\left|x+3\right|+\left|x+5\right|\ge4\)
c, \(\left|x-1\right|+2\left|x-3\right|+\left|x-5\right|\ge4\)
Cần gấp lời giải đầy đủ dễ hiểu và đáp án nhé
\(\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+6\right)}=\frac{1}{8}\)
Bài 2 :
a, \(\frac{3}{\left(x+2\right)\left(x+5\right)}+\frac{5}{\left(x+5\right)\left(x+10\right)}+\frac{7}{\left(x+10\right)\left(x+17\right)}=\frac{x}{\left(x+2\right)\left(x+17\right)}\)
b, \(\frac{2}{\left(x-1\right)\left(x-3\right)}+\frac{5}{\left(x-3\right)\left(x-8\right)}+\frac{12}{\left(x-8\right)\left(x-20\right)}-\frac{1}{\left(x-20\right)}=\frac{-3}{4}\)
Tìm x, biết:
\(\frac{3}{\left(x+2\right)\left(x+5\right)}+\frac{5}{\left(x+5\right)\left(x+10\right)}+\frac{7}{\left(x+10\right)\left(x+17\right)}=\frac{x}{\left(x+2\right)\left(x+17\right)}\left(x\notin-2;-5;-10;-17\right)\)
\(\frac{2}{\left(x-1\right)\left(x-3\right)}+\frac{5}{\left(x-3\right)\left(x-8\right)}+\frac{12}{\left(x-8\right)\left(x-20\right)}-\frac{1}{x-20}=-\frac{3}{4}\)
Với \(x\notin1;3;8;20\)
\(\frac{x+1}{10}+\frac{2+1}{11}\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\frac{x-10}{30}+\frac{x-14}{43}+\frac{x-5}{95}+\frac{x-148}{8}=0\)
A) \(\frac{3}{\left(X+2\right)\left(X+5\right)}\)+\(\frac{5}{\left(X+5\right)\left(X+7\right)}+\frac{7}{\left(X+10\right)\left(X+17\right)}=\frac{X}{\left(X+2\right)\left(X+17\right)}\)
B) \(\frac{2}{\left(X-1\right)\left(X-3\right)}+\frac{5}{\left(X-3\right)\left(x-8\right)}+\frac{12}{\left(X-8\right)\left(X-20\right)}-\frac{-1}{X-20}=\frac{3}{4}\)
Tìm x:
a) \(\dfrac{1}{3}.x+\dfrac{2}{5}\left(x-1\right)=0\)
b)\(-5.\left(x+\dfrac{1}{5}\right)-\dfrac{1}{2}.\left(x-\dfrac{2}{3}\right)=x\)
c)\(\left(x+\dfrac{1}{2}\right).\left(\dfrac{2}{3}-2x\right)=0\)
d)\(9.\left(3x+1\right)^2=16\)
Tìm x
1) 70 : \(\frac{4x+720}{x}\) = 1/2
2) \(\frac{3}{\left(x+2\right)\left(x+5\right)}+\frac{5}{\left(x+5\right)\left(x+10\right)}+\frac{7}{\left(x+10\right)\left(x+17\right)}=\frac{x}{\left(x+2\right)\left(x+17\right)}\) Với x không thuộc { -2; -5; -10; -17 }
Tìm số nguyên x , biết
\(10\) ⋮ \(\left(x-1\right)\)
\(b.\left(x+5\right)\) ⋮ \(\left(x-2\right)\)
c. \(\left(3x+8\right)\) ⋮ \(\left(x-1\right)\)
Nhờ mn giúp mik với ạ
Tìm GTNN
A= \(\left(x-3y\right)^2+\left(2x-1\right)^4\)
B= \(\left|x-2\right|+\left|3x-2y\right|-4\)
C= \(\dfrac{-4}{\left|x+1\right|\left|y-3\right|+2}\)
D=\(\left|x-5\right|+\left|x-1\right|+7\)
