Factor.
y^6 - 9y^4 - 4y^2 = -36
y^6 - 9y^4 - 4y^2 = -36
-
y^6 - 9y^4 - 4y^2 +36 = 0
Now factor it by grouping the polynomial:
(y^6 - 9y^4) + (- 4y^2 +36) = 0
y^4(y^2 -9) -4(y^2 -9) = 0
The y^4 and -4 goes together like so
(y^4 -4)(y^2 -9) = 0
Factor again
(y^2-2)(y^2+2)(y+3)(y-3) = 0
Set each to zero and solve
y^2-2=0
y=±√ 2
y^2+2=0
y=√ -2
y= ± i √2
y-3=0
y=3
y+3=0
y=-3
--------------------------------------…
y = ±√ 2, ± i √2, -3, 3
Now factor it by grouping the polynomial:
(y^6 - 9y^4) + (- 4y^2 +36) = 0
y^4(y^2 -9) -4(y^2 -9) = 0
The y^4 and -4 goes together like so
(y^4 -4)(y^2 -9) = 0
Factor again
(y^2-2)(y^2+2)(y+3)(y-3) = 0
Set each to zero and solve
y^2-2=0
y=±√ 2
y^2+2=0
y=√ -2
y= ± i √2
y-3=0
y=3
y+3=0
y=-3
--------------------------------------…
y = ±√ 2, ± i √2, -3, 3
-
y^6 - 9y^4 - 4y^2 + 36 = 0
y^4 * (y^2 - 9) - 4 * (y^2 - 9) = 0
(y^4 - 4) * (y^2 - 9) = 0
(y^2 - 2) * (y^2 + 2) * (y - 3) * (y + 3) = 0
y^2 - 2 = 0
y^2 = 2
y = -sqrt(2) , sqrt(2)
y^2 + 2 = 0
y^2 = -2
y = -i * sqrt(2) , i * sqrt(2)
y - 3 = 0
y = 3
y + 3 = 0
y = -3
y = -sqrt(2) , sqrt(2) , -3 , 3 , -i * sqrt(2) , i * sqrt(2)
y^4 * (y^2 - 9) - 4 * (y^2 - 9) = 0
(y^4 - 4) * (y^2 - 9) = 0
(y^2 - 2) * (y^2 + 2) * (y - 3) * (y + 3) = 0
y^2 - 2 = 0
y^2 = 2
y = -sqrt(2) , sqrt(2)
y^2 + 2 = 0
y^2 = -2
y = -i * sqrt(2) , i * sqrt(2)
y - 3 = 0
y = 3
y + 3 = 0
y = -3
y = -sqrt(2) , sqrt(2) , -3 , 3 , -i * sqrt(2) , i * sqrt(2)