Ta có:
x^2+3y^2=84:
84 và 3y^2 chia hết cho 3
=> x^2 chia hết cho 3=>x chia hết cho 3=>x E {0;3;6;9}
+)x=0=>3y^2=84=>y^2=28 (loại)
+)x=3=>3y^2=75=>y^2=25=>y=5 (t/m)
+)x=6=>3y^2=48=>y^2=16=>y=4(t/m)
+)x=9=>3y^2=3=>y^2=1=>y=1(t/m)
Vậy có 3 cặp (x,y) E {(3;5);(6;4);(9;1)}
\(x^2+3\cdot y^2=84\)
Ta có : \(3\cdot y^2\le84\)
\(\Rightarrow y^2\le28\)
Vì \(x;y\inℕ\)nên :
Khi \(y^2=25\Rightarrow\hept{\begin{cases}y=5\\x=3\end{cases}}\)
Khi \(y^2=16\Rightarrow\hept{\begin{cases}y=4\\x=6\end{cases}}\)
Khi \(y^2=9\Rightarrow\hept{\begin{cases}y=3\\x=\sqrt{57}\notinℕ\end{cases}}\)
Khi \(y^2=4\Rightarrow\hept{\begin{cases}y=2\\x=\sqrt{72}\notinℕ\end{cases}}\)
Khi \(y^2=1\Rightarrow\hept{\begin{cases}y=1\\x=9\end{cases}}\)
Vậy \(\left(x;y\right)\in\left\{\left(9;1\right);\left(6;4\right);\left(3;5\right)\right\}\)
