Giải BPT sau
\(\sqrt{x+1}\le\dfrac{x^2-x-2\sqrt[3]{2x+1}}{\sqrt[3]{2x+1}-3}\)
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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 pt và bpt sau:
a)\(\sqrt{x-2\sqrt{x-1}}\)=\(\sqrt{2}\)
b)\(\dfrac{4}{3}\sqrt{16\left(2-2x\right)^3}>24\)
a,ĐK: x\(\ge\)1
⇔\(\sqrt{x-1-2\sqrt{x-1}+1}\)=\(\sqrt{2}\)
⇔\(\sqrt{\left(\sqrt{x-1}-1\right)^2}\)=\(\sqrt{2}\)
⇔\(\left|\sqrt{x-1}-1\right|\)=\(\sqrt{2}\)
TH1:\(\sqrt{x-1}\)-1≥0⇒\(\left|\sqrt{x-1}-1\right|\)=\(\sqrt{x-1}\)-1 bn tự giải ra nha
TH2:\(\sqrt{x-1}\)-1<0⇒\(\left|\sqrt{x-1}-1\right|\)=1-\(\sqrt{x-1}\) bn tự lm nha
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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: \(\dfrac{\left(3-2x-x^2\right)\sqrt{2x-1}}{\sqrt{2x-1}}\)≥0
\(\sqrt{2x-1}\ge0\)
\(\Rightarrow BPT\ge0\) khi
\(3-2x-x^2\ge0\)
\(\Leftrightarrow x^2+2x-3\le0\)
\(\Leftrightarrow\left(x+1\right)^2-4\le0\)
\(\Leftrightarrow\left(x+1\right)^2\le4\)
\(\Leftrightarrow x+1\le2\)
\(\Rightarrow x\le1\)
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Giải các bất phương trình sau:
1. \(\sqrt{5x+1}-\sqrt{4x-1}< 3\sqrt{x}\)
2. \(\sqrt{x+2}-\sqrt{3-x}< \sqrt{5-2x}\)
3 \(\dfrac{\sqrt{12+x-x^2}}{x-11}\ge\dfrac{\sqrt{12+x-x^2}}{2x-9}\)
4.\(\sqrt{x^2-8x+15}+\sqrt{x^2+2x-15}\le\sqrt{4x^2-18x+18}\).
1.ĐK: \(x\ge\dfrac{1}{4}\)
bpt\(\Leftrightarrow5x+1+4x-1-2\sqrt{20x^2-x-1}< 9x\)
\(\Leftrightarrow2\sqrt{20x^2-x-1}>0\)
\(\Leftrightarrow20x^2-x-1>0\)
\(\Leftrightarrow\left[{}\begin{matrix}x< \dfrac{-1}{5}\\x>\dfrac{1}{4}\end{matrix}\right.\)
2.ĐK: \(-2\le x\le\dfrac{5}{2}\)
bpt\(\Leftrightarrow x+2+3-x-2\sqrt{-x^2+x+6}< 5-2x\)
\(\Leftrightarrow2x< 2\sqrt{-x^2+x+6}\)
\(\Leftrightarrow x^2< -x^2+x+6\)
\(\Leftrightarrow-2x^2+x+6>0\)
\(\Leftrightarrow\dfrac{-3}{2}< x< 2\)
3. ĐK: \(\left\{{}\begin{matrix}12+x-x^2\ge0\\x\ne11\\x\ne\dfrac{9}{2}\end{matrix}\right.\)
.bpt\(\Leftrightarrow\sqrt{12+x-x^2}\left(\dfrac{1}{x-11}-\dfrac{1}{2x-9}\right)\ge0\)
\(\Leftrightarrow\sqrt{-x^2+x+12}.\dfrac{x+2}{\left(x-11\right)\left(2x-9\right)}\ge0\)
\(\Rightarrow\dfrac{x+2}{\left(x-11\right)\left(2x-9\right)}\ge0\)
\(\Leftrightarrow\dfrac{x+2}{2x^2-31x+99}\ge0\)
*Xét TH1: \(\left\{{}\begin{matrix}x+2\ge0\\2x^2-31x+99>0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-2\\\left[{}\begin{matrix}x< \dfrac{9}{2}\\x>11\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}-2\le x< \dfrac{9}{2}\\x>11\end{matrix}\right.\)
*Xét TH2: \(\left\{{}\begin{matrix}x+2\le0\\2x^2-31x+99< 0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\le-2\\\dfrac{9}{2}< x< 11\end{matrix}\right.\)\(\Rightarrow\dfrac{9}{2}< x< 11\)
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giải bất phương trình:
\(\sqrt{x+1}\le\dfrac{x^2-x-2\sqrt[3]{2x+1}}{\sqrt[3]{2x+1}-3}\)
Giải bpt:
a,\(\frac{\sqrt{x^2-x+4}-2x-3}{x-2}>3\)
b, \(\sqrt{x\left(x-1\right)}+\sqrt{x\left(x+2\right)}\le\sqrt{x\left(4x+1\right)}\)