Question

Tìm x:

x^4+x^2-20=0

Tính giá trị biểu thức :

2014²-4028.1014+1014²

Answer 1

\(x^4+x^2-20=0\)

\(\Leftrightarrow x^4-4x^2+5x^2-20=0\)

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

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

Dễ thấy \(x^2+5>0\Rightarrow x^2+5=0\left(loại\right)\)

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

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

\(\Leftrightarrow x=\pm2\)