найти целые значения уравнения x^2-xy-2y^2=1. помогите !!). Created by lyushka. algebra-ru

найти целые значения уравнения x^2-xy-2y^2=1. помогите !!)...

lyushka @lyushka

July 2022 1 5 Report

найти целые значения уравнения x^2-xy-2y^2=1. помогите !!)

Answers & Comments

arsenlevadniy

Verified answer

$x^2-xy-2y^2=1, \\ x\in Z, y\in Z; \\
x^2-2\cdot x\cdot\frac{1}{2}y+(\frac{1}{2}y)^2-(\frac{1}{2}y)^2-2y^2=1, \\ 
(x-\frac{1}{2}y)^2-\frac{1}{4}y^2-2y^2=1, \\ 
(x-\frac{1}{2}y)^2-\frac{9}{4}y^2=1, \\ (x-\frac{1}{2}y)^2-(\frac{3}{2}y)^2=1, \\ (x-\frac{1}{2}y-\frac{3}{2}y)(x-\frac{1}{2}y+\frac{3}{2}y)=1, \\ (x-2y)(x+y)=1, \\ (x-2y)\in Z, (x+y)\in Z, \\ \left \{ {{x-2y=1,} \atop {x+y=1;}} \right. \left \{ {{3x=3,} \atop {-3y=0;}} \right. \left \{ {{x=1,} \atop {y=0.}} \right.$

0 votes Thanks 4

Voriak http://tex.z-dn.net/?f=x%5E2-xy-2y%5E2%3D1%2C+%5C%5C+x%5Cin+Z%2C+y%5Cin+Z%3B+%5C%5C%0Ax%5E2-2%5Ccdot+x%5Ccdot%5Cfrac%7B1%7D%7B2%7Dy%2B%28%5Cfrac%7B1%7D%7B2%7Dy%29%5E2-%28%5Cfrac%7B1%7D%7B2%7Dy%29%5E2-2y%5E2%3D1%2C+%5C%5C+%0A%28x-%5Cfrac%7B1%7D%7B2%7Dy%29%5E2-%5Cfrac%7B1%7D%7B4%7Dy%5E2-2y%5E2%3D1%2C+%5C%5C+%0A%28x-%5Cfrac%7B1%7D%7B2%7Dy%29%5E2-%5Cfrac%7B9%7D%7B4%7Dy%5E2%3D1%2C+%5C%5C+%28x-%5Cfrac%7B1%7D%7B2%7Dy%29%5E2-%28%5Cfrac%7B3%7D%7B2%7Dy%29%5E2%3D1%2C+%5C%5C+%28x-%5Cfrac%7B1%7D%7B2%7Dy-%5Cf

Answers & Comments

Verified answer

pomogitepozhalujsta3voproszaraneespasibo

pomogite pozhalujsta dvizhenie mnogokletochnyh zhivotnyh stroenie ih oporno dviga

stroenie semyan 1 i 2 dolnyh rastenij pozhalujsta zaranee spasibo

biologicheskaya rol socvetiya

opisanie zdorovogo cheloveka po sleduyushim parametram vneshnij vid pohodka povedeni

рекомендуемые вопросы

Helpful Links

Helpful Social