I need help on solving this equation.

Question

3y⁴ − 7y² + 1 = 0

 

 

I am supposed to get 4 answers according to my notes. 

Answer 1

Rewrite as 3x² - 7x + 1 =0 where x = y²

Since the equation cannot be factored, we use the quadratic formula.

7 ± sqrt(49 - 4(3)(1))/6

7 ± sqrt(37)/6

 

x = 7+sqrt(37)/6 and 7-sqrt(37)/6

 

These are your x-values. We want to express them in terms of y which is just y = sqrt(x)

Since we square root the x values, each x value has two y values

y = ± sqrt(7+sqrt(37)/6) and ± sqrt(7-sqrt(37)/6)