1. Find one pair $(x, y)$ of real numbers such that $x + y = 4$ and $x^3 + y^3 = 100.$ 2.For what real values of $k$ does the quadratic $12x^2 + kx + 27 = 0$ have nonreal roots? Enter your answer as an interval.
3.Find all pairs $(x, y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 56$.
4.Simplify $\displaystyle\frac{1-i}{2+3i}$, where $i^2 = -1.$
5.What is the smallest value of $x$ that satisfies the equation $8x^2 - 38x + 35 = 0$? Express your answer as a decimal.