Question

Solve
w^4-6w^2-2=0

Answer 1

Let
\[y=w^2\]
\[w^4-6w^2-2=0 \Leftrightarrow y^2-6y-2=0\]
solve with quadratic formula.
\[you\ get\ two\ roots:\ y_{1}\ and\ y_{2} \]
The equation is of the fourth degree for w so you'll have four solutions for w, so
\[since\ w^2=y \Leftrightarrow w=y\ or\ w=-y \Leftrightarrow w_{1}=y_{1},w_{2}=-y_{1},w_{3}=y_{2},w_{4}=-y_{2}\]