We know x and y are positive integers; we need to compare the value of $\(\mathrm{x}^2+\mathrm{y}^2\)$ with \(xy\)

The column A expression being addition of the square of $\(x\)$ and $\(y\)$ i.e. $\(x \times x+y \times y\)$ must be greater than the product of x and y .

The same can also be proved by taking different values for $\(x\)$ and $\(y\)$.

Taking $\(x=y\)$, we get column $\(A=x^2+y^2=x^2+x^2=2 x^2\)$ which is clearly greater than column $\(B\)$ expression $\(x y=x \times x=x^2\)$. Next even if consider $\(x\)$ and $\(y\)$ different say $\(x=2\)$ and


$\(y=3\)$, we get column $\(\mathrm{A}=\mathrm{x}^2+\mathrm{y}^2=2^2+3^2=4+9=13\)$ and column $\(\mathrm{B}=\mathrm{xy}=2 \times 3=6\)$.

Hence in all possible cases column A has higher quantity, so the answer is (A).