แก้โจทย์ left(10xright)^2+10x+8=3p^2+10x-11

$${ \left(10x \right) }^{ 2 } +10x+8 = 3 { p }^{ 2 } +10x-11$$

หาค่า x (complex solution)

$$x=-\frac{\sqrt{3p^{2}-19}}{10}$$

$$x=\frac{\sqrt{3p^{2}-19}}{10}$$

หาค่า p

$$p=\frac{\sqrt{300x^{2}+57}}{3}$$

$$p=-\frac{\sqrt{300x^{2}+57}}{3}$$

หาค่า x

$$x=-\frac{\sqrt{3p^{2}-19}}{10}$$

$$x=\frac{\sqrt{3p^{2}-19}}{10}\text{, }|p|\geq \frac{\sqrt{57}}{3}$$