If $x+y=3$ and $xy=2$,then find the value of $x^3-y^3$.

The least integer $k$ which makes the roots of the equation ${x^2} + 5x + k = 0$ imaginary is

If the expression $\left( mx - 1 + \frac{1}{x} \right)$ is always non-negative for $x > 0$,then the minimum value of $m$ must be

The expression $x^2-x+1$ has:

Solve the given two equations and select the correct answer from the given options.
$I.$ $4x + 7y = 209$
$II.$ $12x - 14y = -38$

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: