Question

Giải hệ bpt:

a. \(\left\{{}\begin{matrix}x^2+6x+5>0\\x^2+x-6< 0\end{matrix}\right.\)

b. \(\left\{{}\begin{matrix}2x^2+x-6>0\\3x^2+3\ge10x\end{matrix}\right.\)

Answer 1

a: =>(x+1)(x+5)>0 và (x+3)(x-2)<0

=>\(\left\{{}\begin{matrix}x\in\left(-\infty;-5\right)\cup\left(-1;+\infty\right)\\x\in\left(-3;2\right)\end{matrix}\right.\Leftrightarrow x\in\left(-1;2\right)\)

b: =>(x+2)(2x-3)>0và 3x^2-10x+3>=0

=>(x+2)(2x-3)>0 và (x-3)(3x-1)>=0

=>\(\left\{{}\begin{matrix}x\in\left(-\infty;-2\right)\cup\left(\dfrac{3}{2};+\infty\right)\\x\in(-\infty;\dfrac{1}{3}]\cup[3;+\infty)\end{matrix}\right.\Leftrightarrow x\in\left(-\infty;-2\right)\cup[3;+\infty)\)