Question

Найти пары целых чисел, удовлетворяющих уравнению:
x^2+4x=y^2+3

Answer 1

х²+4х=у²+3

(х+2)²-4-у²=3

(х+2-у)(х+2+у)=7

1. (х+2-у)=7; (х+2+у)=1⇒2х+4=8; х=2,у=1-2-х=--3. (2;-3)

2. (х+2-у)=1; (х+2+у)=7⇒2х+4=8, х=2, у=7-х-2=3, (2;3)

3. (х+2-у)=-1; (х+2+у)=-7; 2х+4=-8; х=-6; у=-7-2-х=-3, (-6;-3)

4. (х+2-у)=-7; (х+2+у)=-1; 2х+4=-8; х=-6, у=-1-2-х=3. (3;-6)