Factor and find all roots: 16x^8-17x^4+1=0

Question

Please help! An explanation on how to get the answer would be most useful!

Answer 1

Hint: Would you know how to solve it if you had a quadratic equation, using the quadratic formula?

Let x⁴ = y

Note that the problem becomes a quadratic equation in y:

16y² - 17y + 1 = 0

No solve for y, and then

x = y^1/4