Answer:
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
