\(x^4-2x^2-114x-1295=0\)
\(\Leftrightarrow\left(x^4+2x^2+1\right)-\left(4x^2+144x+1296\right)=0\)
\(\Leftrightarrow\left(x^2+1\right)^2-\left(2x+36\right)^2=0\)
\(\Leftrightarrow\left(x^2+1-2x-36\right)\left(x^2+1+2x+36\right)=0\)
\(\Leftrightarrow\left(x^2-2x-35\right)\left(x^2+2x+37\right)=0\)
\(\Leftrightarrow\left(x^2+5x-7x-35\right)\left(x^2+2x+1+36\right)=0\)
\(\Leftrightarrow\left[\left(x^2+5x\right)-\left(7x+35\right)\right]\left[\left(x+1\right)^2+36\right]=0\)
\(\Leftrightarrow\left[x\left(x+5\right)-7\left(x+5\right)\right]\left[\left(x+1\right)^2+36\right]=0\)
\(\Leftrightarrow\left(x-7\right)\left(x+5\right)\left[\left(x+1\right)^2+36\right]=0\)
Ta có: \(\left(x+1\right)^2+36>0\) với mọi x thuộc R
Suy ra: \(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-5\end{matrix}\right.\)
Vậy......................
