/ ____________\ / ____________\ / ____________\ / ____________\
| / ____ | | / ____ | | / ____ | | / ____ |
| / 9 \/ 65 | | / 9 \/ 65 | | / 9 \/ 65 | | / 9 \/ 65 |
|x + / - - ------ |*|x - / - - ------ |*|x + / - + ------ |*|x - / - + ------ |
\ \/ 2 2 / \ \/ 2 2 / \ \/ 2 2 / \ \/ 2 2 /
$$\left(x - \sqrt{\frac{9}{2} - \frac{\sqrt{65}}{2}}\right) \left(x + \sqrt{\frac{9}{2} - \frac{\sqrt{65}}{2}}\right) \left(x + \sqrt{\frac{\sqrt{65}}{2} + \frac{9}{2}}\right) \left(x - \sqrt{\frac{\sqrt{65}}{2} + \frac{9}{2}}\right)$$
(((x + sqrt(9/2 - sqrt(65)/2))*(x - sqrt(9/2 - sqrt(65)/2)))*(x + sqrt(9/2 + sqrt(65)/2)))*(x - sqrt(9/2 + sqrt(65)/2))
Expresión del cuadrado perfecto
Expresemos el cuadrado perfecto del trinomio cuadrático
$$\left(y^{4} - 9 y^{2}\right) + 4$$
Para eso usemos la fórmula
$$a y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n$$
donde
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
En nuestro caso
$$a = 1$$
$$b = -9$$
$$c = 4$$
Entonces
$$m = - \frac{9}{2}$$
$$n = - \frac{65}{4}$$
Pues,
$$\left(y^{2} - \frac{9}{2}\right)^{2} - \frac{65}{4}$$