ĐKXĐ: \(x\ge\frac{2}{3}\)
\(\Leftrightarrow\sqrt{x+2}-2+x-\sqrt{3x-2}+x^2-2x\le0\)
\(\Leftrightarrow\frac{x-2}{\sqrt{x+2}+2}+\frac{x^2-3x+2}{x+\sqrt{3x-2}}+x\left(x-2\right)\le0\)
\(\Leftrightarrow\left(x-2\right)\left(\frac{1}{\sqrt{x+2}+2}+\frac{x-1}{x+\sqrt{3x-2}}+x\right)\le0\)
\(\Leftrightarrow x-2\le0\Rightarrow x\le2\)
Vậy nghiệm của BPT là: \(\frac{2}{3}\le x\le2\)
Giải bpt
\(\dfrac{1}{\sqrt{x^2+1}}+\dfrac{1}{\sqrt{3x^2+5}}\le\dfrac{2}{\sqrt{x^2-2}+1}\)
1 giải bpt \(\sqrt{6x^2-18x+12}< 3x+10-x^2\)
2 giải bpt \(\left(x-2\right)\sqrt{x^2+4}\le x^2-4\)
Giải BPT
\(\frac{\sqrt{-x^2+x+6}}{2x+5}\le\frac{\sqrt{-x^2+x+6}}{x+4}\)
giải bpt
1.\(\frac{1}{x+2}\ge\frac{x+2}{3x-5}\)
2.\(\sqrt{-x^2+4x-3}\le x-1\)
help!
giải bpt:
1. \(\frac{\sqrt{-3x^2+x+4}+2}{x}< 2\)
2. \(\sqrt{x^2-3x+2}+\sqrt{x^2-4x+3}\ge2\sqrt{x^2-5x+4}\)
3. \(\sqrt{x^2-8x+15}+\sqrt{x^2+2x-15}\le\sqrt{4x^2-18x=18}\)
4. 4(x+1)2 \(\ge\) (2x +10)( 1- \(\sqrt{3+2x}\))2
5. \(\sqrt{1+x}-\sqrt{1-x}\ge x\)
Giải bpt
\(\sqrt{x^2-3x+3}+\sqrt{x^2-3x+6}\ge3\)
giúp mình giải bpt vs
\(\dfrac{\left|2x-1\right|-x}{2x}>1;\dfrac{2-\left|x-2\right|}{x^2-1}\ge0;\dfrac{\sqrt{x+4}-2}{4-9x^2}\le0;\dfrac{x^2-2x-3}{\sqrt[3]{3x-1}+\sqrt[3]{4-5x}}\ge0;\)\(3x^2-10x+3\ge0;\left(\sqrt{2}-x\right)\left(x^2-2\right)\left(2x-4\right)< 0;\dfrac{1}{x+9}-\dfrac{1}{x}>\dfrac{1}{2};\dfrac{2}{1-2x}\le\dfrac{3}{x+1}\)
tính tổng các nghiệm thuộc [-5;5] của BPT:
\(\sqrt{x^2-9}\left(\frac{3x-1}{x+5}\right)\le x\sqrt{x^2-9}\)
Giải bpt:
a,\(\frac{\sqrt{x^2-x+4}-2x-3}{x-2}>3\)
b, \(\sqrt{x\left(x-1\right)}+\sqrt{x\left(x+2\right)}\le\sqrt{x\left(4x+1\right)}\)
