Let $X=\{(x,y):x^2+2y^2=3,\ x,y\in Z\}$ and $Y=\{(x,y):x>y,\ x,y\in Z\}$. The number of elements in $X\cap Y$ is

✅ Correct Answer: 1

Explanation

Solutions of $x^2+2y^2=3$ are $(1,1),(1,-1),(-1,1),(-1,-1)$ From these, only $(1,-1)$ satisfies $x>y$ So $n(X \cap Y)=1$

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Let $X=\{(x,y):x^2+2y^2=3,\ x,y\in Z\}$ and $Y=\{(x,y):x>y,\ x,y\in Z\}$. The number of elements in $X\cap Y$ is | ACME Academy