## mathtard 4 years ago w^4-14w^2-2=0 solve

1. anonymous

gimmick is to put $x=w^2$ and write $x^2-14x-2=0$ solve for x

2. anonymous

then go back. solve for x via $x^2-14x=2$ $(x-7)^2=2+49$ $(x-7)^2=51$ $x-7=\pm\sqrt{51}$ $x=7\pm\sqrt{51}$

3. anonymous

now $7-\sqrt{51}<0$ so you cannot have $w^2=7-\sqrt{51}$ with real numbers. therefore $w^2=7+\sqrt{51}$ and finally $w=\pm\sqrt{7+\sqrt{51}}$

4. mathtard

thank you!

5. anonymous

yw