Question

giải cac bất phương trình sau:

1) 6x²-x-1<0

2) -2x²+7x-6>0

3) 25x²-30x+9>0

4) -3x²+x-5<0

5) 2x²-4x+7≥0

6) 8x²+23x+14≤0

7) x²-2x+3>0

8) 6x²-x-2≥0

9) \(\frac{1}{3}\)x²+3x+6<0

10) x²+9>6x

giup em với mng!!!

Answer 1

1. \(\Leftrightarrow\left(2x-1\right)\left(3x+1\right)< 0\)

\(\Rightarrow-\frac{1}{3}< x< \frac{1}{2}\)

2. \(\Leftrightarrow\left(x-2\right)\left(3-2x\right)>0\)

\(\Rightarrow\frac{3}{2}< x< 2\)

3. \(\Leftrightarrow\left(5x-3\right)^2>0\)

\(\Rightarrow x\ne\frac{3}{5}\)

4. \(\Leftrightarrow-3\left(x-\frac{1}{6}\right)-\frac{59}{12}< 0\)

\(\Rightarrow x\in R\)

5. \(\Leftrightarrow2\left(x-1\right)^2+5\ge0\)

\(\Rightarrow x\in R\)

Answer 2

6. \(\Leftrightarrow\left(x+2\right)\left(8x+7\right)\le0\)

\(\Rightarrow-2\le x\le-\frac{7}{8}\)

7.

\(\Leftrightarrow\left(x-1\right)^2+2>0\)

\(\Rightarrow x\in R\)

8. \(\Leftrightarrow\left(3x-2\right)\left(2x+1\right)\ge0\)

\(\Rightarrow\left[{}\begin{matrix}x\le-\frac{1}{2}\\x\ge\frac{2}{3}\end{matrix}\right.\)

9. \(\Leftrightarrow\frac{1}{3}\left(x+3\right)\left(x+6\right)< 0\)

\(\Rightarrow-6< x< -3\)

10. \(\Leftrightarrow x^2-6x+9>0\)

\(\Leftrightarrow\left(x-3\right)^2>0\)

\(\Rightarrow x\ne3\)