Question and Answers Forum

All Questions      Topic List

Number Theory Questions

Previous in All Question      Next in All Question      

Previous in Number Theory      Next in Number Theory      

Question Number 162169 by Rasheed.Sindhi last updated on 27/Dec/21

$$$$$$\overline{)\begin{array}{c}\stackrel{\bullet }{{\overline{)\begin{array}{c}\underset{x=?,y=?}{\stackrel{x,y\in \mathbb{Z}}{x+y+x^2{y}^2=586}}\end{array}}}_{}^{}}\end{array}}$$$$$$

Answered by naka3546 last updated on 27/Dec/21

$$(x,y)=(-2,12),(0,586),(12,-2),(586,0)$$

Commented by Rasheed.Sindhi last updated on 27/Dec/21

$$\mathrm{Also}(4,6),(6,4)$$$$\mathbb{T}\mathrm{han}\mathbb{k}\mathrm{you}\mathrm{sir}!Buttheprocess?$$

Answered by Rasheed.Sindhi last updated on 28/Dec/21

$$x+y+x^2{y}^2=586$$$${\left(xy\right)}^2=586-(x+y)$$$$\Rightarrow 586-(x+y)isperfectsquare.$$$$586-(x+y)=a^2$$$$x+y=586-a^2$$$$Fora=\pm 1,\pm 2,\pm 3,...\pm 24$$$$x+y=586-1,586-4,586-9,...586-576$$$$\overline{)\begin{array}{ccccc}a& x+y& x^2{y}^2& xy& z^2-(x+y)z+xy=0\\ 0& 586& 0& 0& z^2-586z=0\\ \pm 1& 585& 1& \pm 1& z^2-585z\pm 1=0\\ \pm 2& 582& 4& \pm 2& z^2-582z\pm 2=0\\ \pm 3& 577& 9& \pm 3& z^2-577z\pm 3=0\\ \pm 4& 570& 16& \pm 4& z^2-570\pm 4=0\\ ...& ...& & & \\ \pm 24& 10& 576& \pm 24& z^2-10z\pm 24=0\end{array}}$$$$Continue...$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com