The equation $\log_e x + \log_e(1 + x) = 0$ can be written as

One root of the equation $3x^2 - 10x + 3 = 0$ is $\frac{1}{3}$. Find the other root.

Which of the following equations has equal roots?

Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{25} x + \sqrt{16} y = 41$
$II.$ $\sqrt{16} x + \sqrt{25} y = 40$

Solve the given two equations and select the correct answer from the given options.
$I.$ $\quad x = \sqrt[3]{2197}$
$II.$ $\quad y^2 = 169$

If $\alpha_1 < \alpha_2 < \alpha_3 < \alpha_4 < \alpha_5 < \alpha_6$,then the equation $(x - \alpha_1)(x - \alpha_3)(x - \alpha_5) + 3(x - \alpha_2)(x - \alpha_4)(x - \alpha_6) = 0$ has :-