(1) The product of two consecutive negative integers is 2550. What is the sum of the two integers?

(2) The expression $3y^2-y-24$ can be written as $(3y + a)(y + b),$ where a and b are integers. What is a-b?

(3) If $(2x + 3y)^2 = 4$ and $xy = -5$, what is the value of $4x^2 + 9y^2$?

(4) Find the largest prime factor of 9951.

(5) If we write $\sqrt{2}+\frac{1}{\sqrt{2}} + \sqrt{3} + \frac{1}{\sqrt{3}}$ in the form $\dfrac{a\sqrt{2} + b\sqrt{3}}{c}$ such that $a$, $b$, and $c$ are positive integers and $c$ is as small as possible, then what is $a+b+c$?

Guest Mar 9, 2021