Question

Determine all natural numbers x,y,z for which the equation 4x2+45y2+9z2-12xy-36yz=25
Is valid and where x

Answer 1

Step-by-step explanation:

have this until the moment, maybe I'm missing something but I think this can help you

4x2+45y2+9z2−12xy−36yz=25

4(x2−3xy+9y²)+9(y²−4yz+z²)=25

Let's rename the terms x²−3xy+9y² and y2−4yz+z² as s and t. We know that as x, y and z must be naturals, then s and t must be integers. So you can start by finding all integers that solve the equation 4s+9t=25. A couple comes to mind, s=4 and t=1.

I know this isn't a full solution but maybe it can help you