is a triangle in the first quadrant of the xy-plane with vertices , and , where and are positive real numbers. If and , then can be written as , where and are coprime positive integers, what is the value of ?
What is ?
In a school, there are more students in Class A than in Class B, and more students in Class B than in Class C. As a reward for good behavior, a teacher decides to give out some sweets. Every student in class C got more sweets than every student in Class B, and every student in Class B got more sweets than every student in Class A. As it turns out, Class A got more sweets than Class B, and Class B got more sweets than Class C. How many sweets were given out in all?
Given the system of equations the value of can be written as where and are positive coprime integers. Find .
An ordered triple of real numbers is called friendly, if each number is equal to the product of the other 2. How many (distinct) friendly triples are there?
Details and assumptions
The numbers need not be pairwise distinct (which means that no two of them are the same).