1) \(x^4\ge\left(x^2+4x+2\right)^2\)
2) \(x^2-7x+10< 0\)
Những câu hỏi liên quan
1) frac{x^2+2x+5}{x+4}ge x-3
2) frac{x^2-3x-1}{2-x}-x
3) frac{3x-47}{3x-1}frac{4x-47}{2x-1}
4) x+frac{9}{x+2}ge4
5) frac{left(x-1right)^3left(x+2right)^4left(x+6right)}{left(x-7right)^3left(x-2right)^2}le0
6) x^4geleft(x^2+4x+2right)^27x^2-7x+10 0
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1) \(\frac{x^2+2x+5}{x+4}\ge x-3\)
2) \(\frac{x^2-3x-1}{2-x}>-x\)
3) \(\frac{3x-47}{3x-1}>\frac{4x-47}{2x-1}\)
4) \(x+\frac{9}{x+2}\ge4\)
5) \(\frac{\left(x-1\right)^3\left(x+2\right)^4\left(x+6\right)}{\left(x-7\right)^3\left(x-2\right)^2}\le0\)
6) \(x^4\ge\left(x^2+4x+2\right)^27x^2-7x+10< 0\)
1.
\(\frac{x^2+2x+5}{x+4}-\left(x-3\right)\ge0\)
\(\Leftrightarrow\frac{x^2+2x+5-\left(x-3\right)\left(x+4\right)}{x+4}\ge0\)
\(\Leftrightarrow\frac{x+17}{x+4}\ge0\Rightarrow\left[{}\begin{matrix}x>-4\\x\le-12\end{matrix}\right.\)
2.
\(\frac{x^2-3x-1}{2-x}+x>0\)
\(\Leftrightarrow\frac{x^2-3x-1+x\left(2-x\right)}{2-x}>0\)
\(\Leftrightarrow\frac{-x-1}{2-x}>0\Rightarrow\left[{}\begin{matrix}x< -1\\x>2\end{matrix}\right.\)
3.
\(\frac{3x-47}{3x-1}-\frac{4x-47}{2x-1}>0\)
\(\Leftrightarrow\frac{\left(3x-47\right)\left(2x-1\right)-\left(4x-47\right)\left(3x-1\right)}{\left(3x-1\right)\left(2x-1\right)}>0\)
\(\Leftrightarrow\frac{-6x\left(x-8\right)}{\left(3x-1\right)\left(2x-1\right)}>0\Rightarrow\left[{}\begin{matrix}0< x< \frac{1}{3}\\\frac{1}{2}< x< 8\end{matrix}\right.\)
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4.
\(\frac{x\left(x+2\right)+9}{x+2}-4\ge0\)
\(\Leftrightarrow\frac{x^2+2x+9-4\left(x+2\right)}{x+2}\ge0\)
\(\Leftrightarrow\frac{x^2-2x+1}{x+2}\ge0\)
\(\Leftrightarrow\frac{\left(x-1\right)^2}{x+2}\ge0\Rightarrow x>-2\)
5.
\(\frac{\left(x-1\right)^3\left(x+2\right)^4\left(x+6\right)}{\left(x-7\right)^3\left(x-2\right)^2}\le0\Rightarrow\left[{}\begin{matrix}x\le-6\\1\le x< 2\\2< x< 7\\x=-2\end{matrix}\right.\)
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Giải các BPT sau:
a) \(x^4\ge\left(x^2+4x+2\right)^2\)
b) \(x^2-7x+10< 0\)
giải bất phương trình
a/\(\frac{x^4-x^2}{x^2+5x+6}\le0\)
b/\(\frac{4x^2+3x-1}{x^2+5x+7}>0\)
c/\(\frac{x^4+x^2+1}{x^2-4x-5}\le0\)
d/\(\frac{-2x^2+7x+7}{x^2-3x-10}\le-1\)
e/\(\frac{2\left(x-4\right)}{\left(x-1\right)\left(x-7\right)}\ge\frac{1}{x-2}\)
1.giải các bpt sau
a.\(\left(x-3\right)\left(x+3\right)\ge x^2-7x+1\)
b.\(\dfrac{1,5-x}{5}\ge\dfrac{4x+5}{2}\)
2.giải các pt sau
\(x^3+1=x.\left(x+1\right)\)
a) \(^{ }\left(7x+4\right)^2-\left(7x-4\right)\left(7x+4\right)\)
b) \(^{ }8\left(x-2\right)-3\left(x^2-4x-5\right)-5x^2\)
c) \(^{^{ }}\left(x+1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(x+1\right)\)
a: Ta có: \(\left(7x+4\right)^2-\left(7x-4\right)\left(7x+4\right)\)
\(=\left(7x+4\right)\left(7x+4-7x+4\right)\)
\(=8\left(7x+4\right)\)
=56x+32
b: Ta có: \(8\left(x-2\right)^2-3\left(x^2-4x-5\right)-5x^2\)
\(=8x^2-32x+32-3x^2+12x+15-5x^2\)
\(=-20x+47\)
c: Ta có: \(\left(x+1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(x+1\right)\)
\(=x^3+3x^2+3x+1-x^3+1-3x^2-3x\)
=2
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Tìm m để hệ bất phương trình : có nghiệm, vô nghiệma)left{{}begin{matrix}x-10mx-30end{matrix}right.b)left{{}begin{matrix}x+4m^2le2mx+13x+22x-1end{matrix}right.c)left{{}begin{matrix}7x-2ge-4x+192x-3m+2 0end{matrix}right.d)left{{}begin{matrix}mx-10left(3m-2right)x-m0end{matrix}right.GIUPS EM ĐI MÀ NĂN NỈ ĐÓ
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Tìm m để hệ bất phương trình : có nghiệm, vô nghiệm
a)\(\left\{{}\begin{matrix}x-1>0\\mx-3>0\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}x+4m^2\le2mx+1\\3x+2>2x-1\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}7x-2\ge-4x+19\\2x-3m+2< 0\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}mx-1>0\\\left(3m-2\right)x-m>0\end{matrix}\right.\)
GIUPS EM ĐI MÀ NĂN NỈ ĐÓ
bài 2: giải các bpt sau:
1) (x-2)(9-x^2)≤0
2) (x^2-x-6)(x^2-3x+2)≥0
3) frac{left(x-2right)left(9-xright)}{x-1}≤0
4) frac{xleft(x^2-3x+2right)}{x+4}≥0
5) frac{left(x+2right)}{left(x+1right)left(x-2right)}0
6) frac{left(x-2right)left(9-x^2right)}{x-1}≥0
7) frac{x^2left(x-3right)}{3x^2+x-4}≥0
8) frac{x^2-3x+2}{9-x}≥0
9) frac{x^2+1}{x^2+3x-10}≤0
10) frac{x^2-9x+14}{x^2+9x+14}≥0
Đọc tiếp
bài 2: giải các bpt sau:
1) (x-2)(\(9-x^2\))≤0
2) (\(x^2-x-6\))(\(x^2-3x+2\))≥0
3) \(\frac{\left(x-2\right)\left(9-x\right)}{x-1}\)≤0
4) \(\frac{x\left(x^2-3x+2\right)}{x+4}\)≥0
5) \(\frac{\left(x+2\right)}{\left(x+1\right)\left(x-2\right)}\)<0
6) \(\frac{\left(x-2\right)\left(9-x^2\right)}{x-1}\)≥0
7) \(\frac{x^2\left(x-3\right)}{3x^2+x-4}\)≥0
8) \(\frac{x^2-3x+2}{9-x}\)≥0
9) \(\frac{x^2+1}{x^2+3x-10}\)≤0
10) \(\frac{x^2-9x+14}{x^2+9x+14}\)≥0
giải các bất phương trình sau:
1) (x-2)(9-x2)≤0
2) (x2-x-6)(x2-3x+2)≥0
3) frac{left(x-2right)left(9-xright)}{x-1}≤0
4) frac{xleft(x^2-3x+2right)}{x+4}≥0
5) frac{left(x+2right)}{left(x+1right)left(x-2right)}0
6) frac{left(x-2right)left(9-x^2right)}{x-1}≥0
7) frac{x^2left(x-3right)}{3x^2+x-4}≥0
8) frac{x^2-3x+2}{9-x}≥0
9) frac{x^2+1}{x^2+3x-10}≤0
10) frac{x^2-9x+14}{x^2+9x+14}≥0
Đọc tiếp
giải các bất phương trình sau:
1) (x-2)(9-x2)≤0
2) (x2-x-6)(x2-3x+2)≥0
3) \(\frac{\left(x-2\right)\left(9-x\right)}{x-1}\)≤0
4) \(\frac{x\left(x^2-3x+2\right)}{x+4}\)≥0
5) \(\frac{\left(x+2\right)}{\left(x+1\right)\left(x-2\right)}\)<0
6) \(\frac{\left(x-2\right)\left(9-x^2\right)}{x-1}\)≥0
7) \(\frac{x^2\left(x-3\right)}{3x^2+x-4}\)≥0
8) \(\frac{x^2-3x+2}{9-x}\)≥0
9) \(\frac{x^2+1}{x^2+3x-10}\)≤0
10) \(\frac{x^2-9x+14}{x^2+9x+14}\)≥0
Giải các PT sau
a,left(9^2-4right)left(x+1right)left(3x+2right)left(x^2-1right)
b,left(x-1right)^2-1+x^2left(1-xright)left(x+3right)
c,left(x^2-1right)left(x+2right)left(x-3right)left(x-1right)left(x^2-4right)left(x+5right)
d,x^4+x^3+x+10
e,x^3-7x+60
f,x^4-4x^3+12x-90
g,x^5-5x^3+4x0
h,x^4-4x^3+3x^2+4x-40
Đọc tiếp
Giải các PT sau
a,\(\left(9^2-4\right)\left(x+1\right)=\left(3x+2\right)\left(x^2-1\right)\)
b,\(\left(x-1\right)^2-1+x^2=\left(1-x\right)\left(x+3\right)\)
c,\(\left(x^2-1\right)\left(x+2\right)\left(x-3\right)=\left(x-1\right)\left(x^2-4\right)\left(x+5\right)\)
d,\(x^4+x^3+x+1=0\)
e,\(x^3-7x+6=0\)
f,\(x^4-4x^3+12x-9=0\)
g,\(x^5-5x^3+4x=0\)
h,\(x^4-4x^3+3x^2+4x-4=0\)