Question

Tìm x,y :

Iv ) 2x mũ 2 - y mũ 2 = -8

Answer 1

\(\left(2x\right)^2-y^2=-8\)

\(\Rightarrow4x^2-y^2=-8\)

\(\Rightarrow\left(2x-y\right)\left(2x+y\right)=-8\)

\(\Rightarrow\left(2x-y\right);\left(2x+y\right)\in=\left\{-1;1;-2;2;-4;4;-8;8\right\}\)

\(\Rightarrow\left(x;y\right)\in=\left\{\left(\dfrac{7}{4};\dfrac{9}{2}\right);\left(-\dfrac{7}{4};-\dfrac{9}{2}\right);\left(\dfrac{1}{2};3\right);\left(-\dfrac{1}{2};-3\right);\left(-\dfrac{1}{2};3\right)\left(\dfrac{1}{2};-3\right);\left(-\dfrac{7}{4};\dfrac{9}{2}\right);\left(\dfrac{7}{4};-\dfrac{9}{2}\right)\right\}\)