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# Algebra

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How many pairs of positive integers (x,y) satisfy x^2-y^2=51+xy?

Jun 14, 2022

#1
+556
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Hello,

$$x^2-y^2=51+xy$$

$$x^2-y^2-xy=51$$

$$x^2-yx-y^2-51=0$$

Solve with the quadratic formula:

$$x_{1,\:2}=\frac{-\left(-y\right)\pm \sqrt{\left(-y\right)^2-4\cdot \:1\cdot \left(-y^2-51\right)}}{2\cdot \:1}$$

$$x_{1,\:2}=\frac{-\left(-y\right)\pm \sqrt{5y^2+204}}{2\cdot \:1}$$.

I think you got $$y$$...

Let me know if you need help becoz this might get very messy.Good luck

Jun 14, 2022
#2
0

Guest Jun 14, 2022
#3
+556
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How was it not helpful, what else do you need?

Vinculum  Jun 14, 2022