Can you solve the system of non-linear equation?

A system of linear equations can be solved easily by many standard methods. Even in high school mathematics courses, students are taught Cramer's rule and the method of Matrix to solve a given set of consistent linear equations up to three variables. More advance methods are taught in the course of linear algebra. But for a given system of non-linear equations, there is no specific method. Different ideas need to be applied across various parts of mathematics to get the solution. Nonetheless using school level mathematics, many interesting problems can be solved. Here we present once such problem, where we have to solve a system of non-linear equation. x^2 -  yz = 3, y^2 - zx = 4 and z^2 - xy = 5 is the system here, we will solve it using elementary ideas. Knowledge of arithmetic progression is essential.

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