1) giải các bpt sau:
a) \(\sqrt{\left(x-1\right)\left(4-x\right)}>x-2\)
b) \(\sqrt{12+x-x^2}\le x-11\)
c) \(\left(x-3\right)\sqrt{x^2-4}\le x^2-9\)
Những câu hỏi liên quan
Giải BPT: \(\sqrt{x^4+x^2+1}+\sqrt{x.\left(x^2-x+1\right)}\le\sqrt{\dfrac{\left(x^2+1\right)^3}{x}}\)
Giải BPT: \(\sqrt{x^4+x^2+1}+\sqrt{x.\left(x^2-x+1\right)}\le\sqrt{\dfrac{\left(x^2+1\right)^3}{x}}\)
Giải BPT: \(\sqrt{x^4+x^2+1}+\sqrt{x.\left(x^2-x+1\right)}\le\sqrt{\dfrac{\left(x^2+1\right)^3}{x}}\)
Giải BPT: \(\sqrt[4]{\left(x-2\right).\left(4-x\right)}+\sqrt[4]{x-2}+\sqrt[4]{4-x}+6x\sqrt{3x}\le x^3+30\)
Giải BPT: \(\sqrt[4]{\left(x-2\right).\left(4-x\right)}+\sqrt[4]{x-2}+\sqrt[4]{4-x}+6x\sqrt{3x}\le x^3+30\)
Giải các bpt
a) \(\sqrt{x^2-4-12}\le x-4\)
b) \(\sqrt{x^2-8x}\ge2\left(X+1\right)\)
C) \(\left(X-2\right).\sqrt{X^2+4}< X^2-4\)
a, ĐK: \(x\ge4;x\le-4\)
\(\sqrt{x^2-4-12}\le x-4\)
\(\Leftrightarrow\sqrt{x^2-16}\le x-4\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-4\ge0\\x^2-16\le\left(x-4\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\x^2-16\le x^2-8x+16\end{matrix}\right.\)
\(\Leftrightarrow x=4\left(tm\right)\)
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b, ĐK: \(x\ge8;x\le0\)
\(\sqrt{x^2-8x}\ge2\left(x+1\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2\left(x+1\right)\ge0\\x^2-8x\ge4\left(x^2+2x+1\right)\end{matrix}\right.\\2\left(x+1\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow x\le\dfrac{-8+2\sqrt{13}}{3}\)
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c, \(\left(x-2\right)\sqrt{x^2+4}< x^2-4\)
\(\Leftrightarrow\left(x-2\right)\left(x+2-\sqrt{x^2+4}\right)>0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2>0\\x+2-\sqrt{x^2+4}< 0\end{matrix}\right.\left(I\right)\text{v}\left\{{}\begin{matrix}x-2< 0\\x+2-\sqrt{x^2+4}>0\end{matrix}\right.\left(II\right)\)
\(\left(I\right)\Leftrightarrow\left\{{}\begin{matrix}x>2\\x+2< \sqrt{x^2+4}\end{matrix}\right.\Leftrightarrow...\)
\(\left(II\right)\Leftrightarrow\left\{{}\begin{matrix}x-2< 0\\x+2-\sqrt{x^2+4}>0\end{matrix}\right.\Leftrightarrow...\)
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Giải bpt:
a,\(\frac{\sqrt{x^2-x+4}-2x-3}{x-2}>3\)
b, \(\sqrt{x\left(x-1\right)}+\sqrt{x\left(x+2\right)}\le\sqrt{x\left(4x+1\right)}\)
1) giải bpt:
\(-4\sqrt{\left(4-x\right)\left(2+x\right)}\le x^2-2x-12\)
giúp mình giải bpt vs
\(\dfrac{\left|2x-1\right|-x}{2x}>1;\dfrac{2-\left|x-2\right|}{x^2-1}\ge0;\dfrac{\sqrt{x+4}-2}{4-9x^2}\le0;\dfrac{x^2-2x-3}{\sqrt[3]{3x-1}+\sqrt[3]{4-5x}}\ge0;\)\(3x^2-10x+3\ge0;\left(\sqrt{2}-x\right)\left(x^2-2\right)\left(2x-4\right)< 0;\dfrac{1}{x+9}-\dfrac{1}{x}>\dfrac{1}{2};\dfrac{2}{1-2x}\le\dfrac{3}{x+1}\)