a: \(x^2+5x-6>0\)
=>\(x^2+6x-x-6>0\)
=>(x+6)(x-1)>0
TH1: \(\left\{{}\begin{matrix}x+6>0\\x-1>0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>-6\\x>1\end{matrix}\right.\)
=>x>1
TH2: \(\left\{{}\begin{matrix}x+6< 0\\x-1< 0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< -6\\x< 1\end{matrix}\right.\)
=>x<-6
b: \(-3x^2+x+2< =0\)
=>\(3x^2-x-2>=0\)
=>\(3x^2-3x+2x-2>=0\)
=>\(\left(x-1\right)\left(3x+2\right)>=0\)
TH1: \(\left\{{}\begin{matrix}x-1>=0\\3x+2>=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>=1\\x>=-\dfrac{2}{3}\end{matrix}\right.\)
=>x>=1
TH2: \(\left\{{}\begin{matrix}x-1< =0\\3x+2< =0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< =1\\x< =-\dfrac{2}{3}\end{matrix}\right.\)
=>\(x< =-\dfrac{2}{3}\)
c: \(x^2+4x+4>=0\)
=>\(x^2+2\cdot x\cdot2+2^2>=0\)
=>\(\left(x+2\right)^2>=0\)(luôn đúng)
=>\(x\in R\)
d: \(x^2+3x+7>0\)
=>\(x^2+2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{19}{4}>0\)
=>\(\left(x+\dfrac{3}{2}\right)^2+\dfrac{19}{4}>0\)(luôn đúng)
=>\(x\in R\)
