The solution of the differential equation $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{\mathrm{x} + {\mathrm{y}}^2}$ is

• y = - x² - 2x - 2 + ce^x

• y = x² + 2x + 2 - ce^x

• x = - y² - 2y + 2 - ce^y

• x = - y² - 2y - 2 + ce^y

The solution of the equation ${\left(3 + 2\sqrt{2}\right)}^{{\mathrm{x}}^{2 }- 8} + {\left(3 + 2\sqrt{2}\right)}^{8 - {\mathrm{x}}^2}$ = 6 are

• $3 \pm 2\sqrt{2}$

• $\pm 1$

• $\pm 3\sqrt{3}, \pm 2\sqrt{2}$

• $\pm 3, \pm \sqrt{7}$

63.

Let T_n denote the number of triangles which can equal to be formed by using the vertices of a regular polygon of n sides. If T_{n + 1} - T_n = 28, then n equals

• 4

• 5

• 6

• 8