/ ______________\ / ______________\ / ____________\ / ____________\
| / ____ | | / ____ | | / ____ | | / ____ |
| / 3 \/ 17 | | / 3 \/ 17 | | / 3 \/ 17 | | / 3 \/ 17 |
|x + I* / - - + ------ |*|x - I* / - - + ------ |*|x + / - + ------ |*|x - / - + ------ |
\ \/ 2 2 / \ \/ 2 2 / \ \/ 2 2 / \ \/ 2 2 /
$$\left(x - i \sqrt{- \frac{3}{2} + \frac{\sqrt{17}}{2}}\right) \left(x + i \sqrt{- \frac{3}{2} + \frac{\sqrt{17}}{2}}\right) \left(x + \sqrt{\frac{3}{2} + \frac{\sqrt{17}}{2}}\right) \left(x - \sqrt{\frac{3}{2} + \frac{\sqrt{17}}{2}}\right)$$
(((x + i*sqrt(-3/2 + sqrt(17)/2))*(x - i*sqrt(-3/2 + sqrt(17)/2)))*(x + sqrt(3/2 + sqrt(17)/2)))*(x - sqrt(3/2 + sqrt(17)/2))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{4} - 3 y^{2}\right) - 2$$
To do this, let's use the formula
$$a y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -3$$
$$c = -2$$
Then
$$m = - \frac{3}{2}$$
$$n = - \frac{17}{4}$$
So,
$$\left(y^{2} - \frac{3}{2}\right)^{2} - \frac{17}{4}$$