Solve the Equation help please!?

Question

3y^4 − 9y^2 + 1 = 0
Thank you!

Answer 1

Given equation is 3y^4 − 9y^2 + 1 = 0

Let us assume that y^2 = t

Therefore the equation becomes 3t^2 - 9t + 1 =0

Applying quadratic formula to find roots we get,

                             t  = [ -b +/- √(b^2 - 4ac)] / 2a                    [ where a=3, b=-9, c=1 ]

                                = [ -(-9) +/- √(9^2 - 4*3*1) ] / 2*3

                                = [9 +/- √(81 - 12) ] / 6

                                = (9 +/- √69) / 6

                                = (3 +/- √69) / 2

                                = (3 + √69) / 2 , (3 - √69) / 2

But y^2 = t => y = +/-√t

                           = +/-√((3 + √69) / 2)   , +/-√((3 - √69) / 2)

Therefore y = √((3 + √69) / 2), -√((3 + √69) / 2), √((3 - √69) / 2) and -√((3 - √69) / 2).