Need clarity on a hard question


I was practicing hard questions and that’s when I ran into this problem. The answer is supposed to be D. You solve it by simplifying the equation to xy=13 then if you consider 13 and 1 as x and y you get the answer C but it does’nt mention it have to be an integer so √13x√13 is also 13. Hence the answer is D.
But the problem is if we substitute ‘√ 13’ as x and y values in the equation given we don’t get 546. So technically is’nt 13 and 1 the only possible value for x and y? and the answer Therefore C?
Hope you understood the way I explained it.

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