giải bpt :
a, \(x^2-3\left|x\right|+2\le0\)
b, \(2x^2-\left|5x-3\right|\le0\)
c, \(\sqrt{\left(x-3\right)\left(8-x\right)}+26\ge-x^2+11x\)
Những câu hỏi liên quan
giúp mình giải bpt vs
\(\dfrac{\left|2x-1\right|-x}{2x}>1;\dfrac{2-\left|x-2\right|}{x^2-1}\ge0;\dfrac{\sqrt{x+4}-2}{4-9x^2}\le0;\dfrac{x^2-2x-3}{\sqrt[3]{3x-1}+\sqrt[3]{4-5x}}\ge0;\)\(3x^2-10x+3\ge0;\left(\sqrt{2}-x\right)\left(x^2-2\right)\left(2x-4\right)< 0;\dfrac{1}{x+9}-\dfrac{1}{x}>\dfrac{1}{2};\dfrac{2}{1-2x}\le\dfrac{3}{x+1}\)
giải các bpt sau
a. \(\left|x^2-2x-8\right|< 2x\)
b. \(x^2+2\left|x+3\right|-10\le0\)
c. \(\left|x^2-3\right|+2x+1\ge0\)
Giải bpt sau:
\(\frac{\left(x-1\right)^3\left(x+2\right)^4\left(x-3\right)^5\left(x+6\right)}{x^2\left(x-7\right)^3}\le0\)
3 tháng 4 2020 lúc 14:54
Giải bất phương trình
1) \(\frac{x^4-1}{x^2+3x}+x^2\ge1\)
2) \(\left(x^4-5x^2+4\right)\left(\frac{x-2}{x}-3\right)\le0\)
3) \(\left(\frac{4}{x}-\frac{2}{x-1}\right)\left(\frac{x^2+1}{x}-2\right)\le0\)
4) \(\left(\sqrt{x^3-4x}-\sqrt{15}\right)\sqrt{\frac{1+x}{x}-2}\le0\)
a/
\(\Leftrightarrow\frac{\left(x^2-1\right)\left(x^2+1\right)}{x^2+3x}+x^2-1\ge0\)
\(\Leftrightarrow\left(x^2-1\right)\left(\frac{x^2+1}{x^2+3x}+1\right)\ge0\)
\(\Leftrightarrow\left(x^2-1\right)\left(\frac{2x^2+3x+1}{x^2+3x}\right)\ge0\)
\(\Leftrightarrow\frac{\left(x-1\right)\left(x+1\right)\left(x+1\right)\left(2x+1\right)}{x\left(x+3\right)}\ge0\)
\(\Leftrightarrow\frac{\left(x-1\right)\left(2x+1\right)\left(x+1\right)^2}{x\left(x+3\right)}\ge0\)
\(\Rightarrow\left[{}\begin{matrix}x< -3\\x=-1\\-\frac{1}{2}\le x< 0\\x\ge1\end{matrix}\right.\)
b/
\(\Leftrightarrow\left(x^2-1\right)\left(x^2-4\right)\left(\frac{-2-2x}{x}\right)\le0\)
\(\Leftrightarrow\frac{-2.\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\left(x+1\right)}{x}\le0\)
\(\Leftrightarrow\frac{\left(x+2\right)\left(x-1\right)\left(x-2\right)\left(x+1\right)^2}{x}\ge0\)
\(\Rightarrow\left[{}\begin{matrix}x\le-2\\x=-1\\0< x\le1\\x\ge2\end{matrix}\right.\)
c/
\(\Leftrightarrow\left(\frac{4\left(x-1\right)-2x}{x\left(x-1\right)}\right)\left(\frac{x^2+1-2x}{x}\right)\le0\)
\(\Leftrightarrow\frac{\left(2x-4\right)\left(x-1\right)^2}{x^2\left(x-1\right)}\le0\)
\(\Leftrightarrow\frac{\left(x-2\right)\left(x-1\right)^2}{x^2\left(x-1\right)}\le0\)
\(\Rightarrow1< x\le2\)
d/
ĐKXĐ: \(\left\{{}\begin{matrix}x^3-4x\ge0\\\frac{1+x}{x}-2\ge0\\x\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\left(x-2\right)\left(x+2\right)\ge0\\\frac{1-x}{x}\ge0\\x\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}-2\le x\le0\\x\ge2\end{matrix}\right.\\0< x\le1\\x\ne0\end{matrix}\right.\)
\(\Rightarrow\) Không tồn tại x thỏa mãn ĐKXĐ
Vậy BPT đã cho vô nghiệm
Giải các hệ bất phương trình:
a) \(\left\{{}\begin{matrix}4x^2-5x-6\le0\\\left(1-x^2\right)\left(4x^2-12x+5\right)>0\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^2-x-2\ge0\\2x^2-11x+9< 0\\x^3-x^2+2x-2>0\end{matrix}\right.\)
c) \(-3\le\frac{x^2-3x-1}{x^2+x+1}< 3\)
Giải các bất phương trình sau:
a/ \(\sqrt{\left(x-3\right)\left(8-x\right)}+26>-x^2+11x\)
b/ \(\left(x+1\right)\left(x+4\right)< 5\sqrt{x^2+5x+28}\)
GIÚP MÌNH VỚI Ạ!!!
giải hệ bpt:
\(\left\{{}\begin{matrix}\frac{x^2+3x-1}{2-x}>-x\\\frac{\left(x-1\right)^3\left(x+2\right)^2\left(x+6\right)}{\left(x-7\right)^3\left(x-2\right)^2}\le0\end{matrix}\right.\)
\(\frac{x^2+3x-1}{2-x}+x>0\Leftrightarrow\frac{5x-1}{2-x}>0\Rightarrow\frac{1}{5}< x< 2\)
\(\frac{\left(x-1\right)^3\left(x+2\right)^2\left(x+6\right)}{\left(x-7\right)^3\left(x-2\right)^2}\le0\Leftrightarrow\left[{}\begin{matrix}x\le-6\\x=-2\\1\le x< 2\\2< x< 7\end{matrix}\right.\)
Kết hợp lại ta có: \(1\le x< 2\)
Giải các bpt sau
a, \(\frac{\left(4-x\right)\left(x^2-2x-15\right)}{2x^2+x+1}\le0\)
b, \(\frac{x^2+x-3}{x^2-4}\ge1\)
tìm x và y biết
a) \(\left|5x+1\right|+\left|6y-8\right|\le0\)
b) \(\left|x+2y\right|+\left|4y-3\right|\le0\)
c) \(\left|x-y+2\right|+\left|2y+1\right|\le0\)