Question

Tìm x biết

a) (x^2 + 5 ) . ( x^2 - 25 ) = 0

b) ( x^2 -5 ) . (x^2 - 25 ) < 0

c) (x-2) . ( x+1) = 0

Answer 1

a, (x² + 5)(x² - 25) = 0

\(\Rightarrow\left[\begin{matrix}x^2+5=0\\x^2+25=0\end{matrix}\right.\Rightarrow\left[\begin{matrix}x^2=-5\left(loại\right)\\x^2=-25\left(loại\right)\end{matrix}\right.\)

Vậy \(x=\varnothing\)

b, (x² - 5)(x² - 25) < 0

<=> x² - 5 và x² - 25 trái dấu

Ta thấy x² - 5 > x² - 25 nên \(\left\{\begin{matrix}x^2-5>0\\x^2-25< 0\end{matrix}\right.\) <=> x < 5

c, (x - 2)(x + 1) = 0

\(\Rightarrow\left[\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=2\\x=-1\end{matrix}\right.\)

Vậy \(x\in\left\{2;-1\right\}\)