Question

Tìm x thuộc Z

a,( \(^{x^2}\) -5) . ( \(^{x^2}\) - 25 ) <0

b, ( x + 5 ) . ( 9 + \(^{x^2}\) ) <0

c, ( x + 3 ) . ( \(^{x^2}\) + 1 ) =0

d, ( x + 5 ) . ( \(^{x^2}\) - 4 ) = 0

Answer 1

a) \(\left(x^2-5\right)\left(x^2-25\right)< 0\)

Vì \(x^2-5>x^2-25\) nên \(\left\{{}\begin{matrix}x^2-5>0\\x^2-25< 0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2>5\\x^2< 25\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{5}< x< -\sqrt{5}\left(vl\right)\\-5< x< 5\end{matrix}\right.\)

b) \(\left(x+5\right)\left(9+x^2\right)< 0\)

Vì \(9+x^2>0\) nên \(x+5< 0\Leftrightarrow x< -5\)

c) \(\left(x+3\right)\left(x^2+1\right)=0\)

Vì \(x^2+1>0\) nên \(x+3=0\Leftrightarrow x=-3\)

d) \(\left(x+5\right)\left(x^2-4\right)=0\)

\(\Rightarrow\left(x+5\right)\left(x+2\right)\left(x-2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=-5\\x=-2\\x=2\end{matrix}\right.\)