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\(a,x\left(x-5\right)+6< 0\Leftrightarrow\left(x+6\right)\left(x-5\right)< 0\)
\(\orbr{\begin{cases}x+6< 0\\x-5< 0\end{cases}\Leftrightarrow\orbr{\begin{cases}x< -6\\x< 5\end{cases}}}\)
\(b,x^2+\left(x-2\right)\left(x+2\right)>2x\left(x-2\right)\)
\(\Leftrightarrow x^2+x^2-4>2x^2-4x\Leftrightarrow-4>-4x\)
\(\Leftrightarrow-4x< -4\Rightarrow x>1\)
\(c,\left(x-3\right)\left(x-3\right)+\left(x+5\right)\left(x+5\right)< 2\left(x-3\left(x+5\right)\right)\)
\(\Leftrightarrow x^2-6x+9+x^2+10x+25< 2x^2+4x-30\)
\(\Leftrightarrow2x^2-2x^2+4x-4x< -30-34\)
\(\Leftrightarrow0x< -64\)
bất phương trình vô nghiệm
\(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)=\left(x-2\right)\left(x+2\right)\)
\(\Rightarrow8x+16-5x^2-10x+4x^2+4x-8x-8=x^2-4\)
\(\Rightarrow-6x-x^2-8-x^2+4=0\)
\(\Rightarrow-6x-2x^2-4=0\)
\(\Rightarrow-2\left(3x+x^2+2\right)=0\)
\(\Rightarrow\left(x+1,5\right)^2-0,25=0\)
\(\Rightarrow\left(x+2\right)\left(x+1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+2=0\\x+1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-2\\x=-1\end{cases}}}\)
a: \(\dfrac{3x-1}{2-5x}< 0\)
\(\Leftrightarrow\dfrac{3x-1}{5x-2}>0\)
=>x>2/5 hoặc x<1/3
b: \(\dfrac{3x-2}{1-2x}< 1\)
\(\Leftrightarrow\dfrac{3x-2-1+2x}{1-2x}< 0\)
\(\Leftrightarrow\dfrac{5x-3}{2x-1}>0\)
=>x>3/5 hoặc x<1/2
c: \(\dfrac{2x\left(3x-5\right)}{x^2+1}< 0\)
=>2x(3x-5)<0
=>x(3x-5)<0
=>0<x<5/3
a) \(2\left(x+5\right)-x^2-5x=0\)
\(\Leftrightarrow2x+10-x^2-5x=0\)
\(\Leftrightarrow-x^2-3x+10=0\)
\(\Leftrightarrow x^2+3x-10=0\)
\(\Leftrightarrow x^2-2x+5x-10=0\)
\(\Leftrightarrow x\left(x-2\right)+5\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x+5=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-5\end{cases}}}\)
b) \(x^3-6x^2+12x-8=0\)
\(\Leftrightarrow\left(x^3-8\right)-\left(6x^2-12x\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2+2x+4\right)-6x\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2+2x+4-6x\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-2\right)^2=0\)
\(\Leftrightarrow\left(x-2\right)^3=0\)
\(\Leftrightarrow x-2=0\Leftrightarrow x=2\)
c)\(16x^2-9\left(x+1\right)^2=0\)
\(\Leftrightarrow\left(4x\right)^2-\left[3\left(x+1\right)\right]^2=0\)
\(\Leftrightarrow\left(4x-3x-1\right)\left(4x+3x+1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(7x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\7x+1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=-\frac{1}{7}\end{cases}}}\)
d) \(x^3+x=0\)
\(\Leftrightarrow x^2\left(x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2=0\\x+1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-1\end{cases}}}\)
e)\(x^2-2x-3=0\)
\(\Leftrightarrow x^2+x-3x-3=0\)
\(\Leftrightarrow x\left(x+1\right)-3\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\x-3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=3\end{cases}}}\)
( x - 1 )( x2 + 5x - 2 ) - ( x3 - 1 ) = 0
<=> ( x - 1 )( x2 + 5x - 2 ) - ( x - 1 )( x2 + x + 1 ) = 0
<=> ( x - 1 )( x2 + 5x - 2 - x2 - x - 1 ) = 0
<=> ( x - 1 )( 4x - 3 ) = 0
<=> x - 1 = 0 hoặc 4x - 3 = 0
<=> x = 1 hoặc x = 3/4
Vậy pt có tập nghiệm S = { 1 ; 3/4 }