Question

Tìm các cặp số nguyên (x;y) thỏa mãn đẳng thức sau :

\(2\left|x\right|+5\left|y\right|=9-\left|x\right|+2\left|y\right|\)

Answer 1

\(2\left|x\right|+5\left|y\right|=9-\left|x\right|+2\left|y\right|\)

\(2\left|x\right|+\left|x\right|+5\left|y\right|-2\left|y\right|=9\)

\(\left|x\right|\left(2+1\right)+\left|y\right|\left(5-2\right)=9\)

\(3\left|x\right|+3\left|y\right|=9\)

\(3.\left(\left|x\right|+\left|y\right|\right)=9\Rightarrow\left|x\right|+\left|y\right|=3\)

Mà : \(\left|x\right|\ge0;\left|y\right|\ge0\)

Ta có : Với \(\left|x\right|=0;\left|y\right|=3\Rightarrow x=0;y\in\left\{-3;3\right\}\)

Với \(\left|x\right|=3;\left|y\right|=0\Rightarrow x\in\left\{-3;3\right\};y=0\)

Với \(\left|x\right|=1;\left|y\right|=2\Rightarrow x\in\left\{-1;1\right\};y\in\left\{-2;2\right\}\)

Với \(\left|x\right|=2;\left|y\right|=1\Rightarrow x\in\left\{-2;2\right\};y\in\left\{-1;1\right\}\)

Vậy ...