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Question

If $f left parenthesis x comma y right parenthesis to the power of minus end exponent square root of x to the power of 2 end exponent plus y to the power of 2 end exponent end root plus square root of left parenthesis x minus 1 right parenthesis to the power of 2 end exponent plus y to the power of 2 end exponent end root plus square root of x to the power of 2 end exponent plus left parenthesis y minus 1 right parenthesis to the power of 2 end exponent end root plus square root of left parenthesis x minus 3 right parenthesis to the power of 2 end exponent plus left parenthesis y minus 4 right parenthesis to the power of 2 end exponent end root comma$ where $x comma y stack I with hat on top R comma$ then the minimum value of $f left parenthesis x comma y right parenthesis$ is

$2 + \sqrt{5}$
$5 + \sqrt{2}$
$5 - \sqrt{2}$
$\sqrt{5} - 2$

The correct answer is: $5 plus square root of 2$

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