Решите уравнение: 10p^4-21=p^2.

\[10p^{4} - 21 = p^{2}\]

\[10p^{4} - p^{2} - 21 = 0\]

\[p^{2} = x \geq 0:\]

\[10x^{2} - x - 21 = 0\]

\[D = 1 + 840 = 841 = 29^{2}\]

\[x_{1} = \frac{(1 - 29)}{20} < 0;\]

\[x_{2} = \frac{1 + 29}{20} = \frac{30}{20} = \frac{3}{2};\]

\[p^{2} = \frac{3}{2}\]

\[p = \pm \sqrt{\frac{3}{2}} = \pm \sqrt{1,5}.\]

\[Ответ:p = \pm \sqrt{1,5}.\]