y^4+16y^2-15=0

Answer 1

(y^2 + 8)^2 = 79

y^2 = -8 ± √79

y = ± √(-8 ± √79)

Answer 2

y⁴ +16 y² -15 = 0

( y² )² +16 y² -15 = 0

Substitute y² = x

x² +16 x -15 = 0

x² +16 x = 15

x² +16 x + 64 = 15 + 64

x² +16 x + 64 = 79

( x + 8 )² = 79

x + 8 = ± √79

x = ± √79 - 8

x₁= - √79 - 8

x₂= √79 - 8

Now:

y² = x

y² = x₁

y² = - √79 - 8

y = ± √( - √79 - 8 )

y = ± √ [ ( - 1 ) ∙ √( √79 + 8 ) ]

y = ± √( - 1 ) ∙ √( √79 + 8 )

y = ± i ∙ √( √79 + 8 )

y₁ = - i ∙ √( √79 + 8 )

y₂ = i ∙ √( √79 + 8 )

y² = x

y² = x₂

y² = √79 - 8

y = ± √(√79 - 8 )

y₃ = - √(√79 - 8 )

y₄ = √( √79 - 8 )

The solutions are:

- i ∙ √( √79 + 8 ) , i ∙ √( √79 + 8 ) , - √( √79 - 8 ) , √( √79 - 8 )