Find all solutions y(real and otherwise)to the equation
y^8+16=17y^4

y=2, y=-2     y = 2i, y= -2i     y = 1, y = -1     y = i,   y = -i

Step-by-step explanation:

y^8+16=17y^4

Subtract 17 y^4 from each side

y^8 - 17 y^4+16=17y^4-17 y^4

y^8 - 17 y^4+16 =0

Let x = y^4

x^2 -17x + 16 =0

Factor

( x-16) ( x-1) =0

Using the zero product property

x-16 =0  x-1 =0

x=16  x=1

Replace x with y^4

y^4 = 16      y^4 = 1

y^4 -16 = 0          y^4 -1 =0

Replace y^2 with z

z^2 -16 =0                       z^2 -1 = 0

( z-4) ( z+4) = 0               ( z-1) = 0   ( z+1) =0

z=4  z=-4                           z=1            z=-1

Replace z with y^2

y^2 = 4   y^2 = -4           y^2 = 1       y^2 = -1

Taking the square root

y=2, y=-2     y = 2i, y= -2i     y = 1, y = -1     y = i,   y = -i