The roots of the equation $x^{2/3} + x^{1/3} - 2 = 0$ are

Let $S$ be the set of all real roots of the equation,$3^{x}(3^{x}-1)+2=|3^{x}-1|+|3^{x}-2|$. Then $S$

Solve the given two equations and select the correct option.
$I. 15x^2 - 46x + 35 = 0$
$II. 4y^2 - 15y + 14 = 0$

Let $\alpha$ and $\beta$ be the roots of $5x^2 - 3x - 1 = 0$. Then,the expression $\left[ (\alpha + \beta)x - \left( \frac{\alpha^2 + \beta^2}{2} \right)x^2 + \left( \frac{\alpha^3 + \beta^3}{3} \right)x^3 - \dots \right]$ is equal to:

Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up with roots $(4, 3).$ Rahul made a mistake in writing down the coefficient of $x$ and got roots $(3, 2).$ The correct roots of the equation are:

If $x = \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ and $y = \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$,then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}} = ?$