Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem19

Levels 11&12 Video Solutions 2013 problem19

Video Transcription

Video Summary

The video transcript discusses solving a mathematical problem involving finding the number of pairs \(x, y\) of positive integers that satisfy the equation \(x^2 y^3 = 6^{12}\). The solution involves prime factorizing \(6^{12}\) into \(2^{12} \times 3^{12}\) and assigning powers \(a, b, c, d\) to the factors of \(x\) and \(y\). By equating powers, two equations \(12 = 2a + 3c\) and \(12 = 2b + 3d\) are solved for positive integer solutions. Ultimately, there are 9 valid pair combinations of \(x, y\), making this the final solution.

Keywords

mathematical problem

positive integers

prime factorization

equation solutions

pair combinations