a) \(\left(x^2-9\right)\left(x^2+7x+14\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+3\right)\left[\left(x+\dfrac{7}{2}\right)^2+\dfrac{7}{4}\right]=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+3\right)=0\) (vì \(\left(x+\dfrac{7}{2}\right)^2+\dfrac{7}{4}>0\forall x\))
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
b) \(x^4-2=0\)
\(\Leftrightarrow\left(x^2-\sqrt{2}\right)\left(x^2+\sqrt{2}\right)=0\)
\(\Leftrightarrow x^2-\sqrt{2}=0\) (vì \(x^2+\sqrt{2}>0\forall x\))
\(\Leftrightarrow\left(x-\sqrt{\sqrt{2}}\right)\left(x+\sqrt{\sqrt{2}}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\sqrt{2}}\\x=-\sqrt{\sqrt{2}}\end{matrix}\right.\)
a)
\(\Leftrightarrow\left(x^2-9\right)\left(x^2+2\cdot\dfrac{7}{2}x+\dfrac{49}{4}+\dfrac{7}{4}\right)=0\)
\(\Leftrightarrow\left(x^2-9\right)\left[\left(x+\dfrac{7}{2}\right)^2+\dfrac{7}{4}\right]=0\)
Vì \(\left(x+\dfrac{7}{2}\right)^2\ge0\Rightarrow\left(x+\dfrac{7}{2}\right)^2+\dfrac{7}{4}>0\)
\(\Rightarrow x^2-9=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
b)
\(\Leftrightarrow\left(x^2-\sqrt{2}\right)\left(x^2+\sqrt{2}\right)=0\)
Vì \(x^2\ge0\Rightarrow x^2+\sqrt{2}>0\)
\(\Rightarrow x^2-\sqrt{2}=0\)
\(\Leftrightarrow x^2=\sqrt{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt[4]{2}\\x=-\sqrt[4]{2}\end{matrix}\right.\)
