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(D) For equation $I$: $x^{2}-82x+781=0$.We need two numbers whose product is $781$ and sum is $82$. These numbers are $71$ and $11$.So,$(x-71)(x-11)=0

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if $x = y$ or relationship between $x$ and $y$ cannot be established.

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(D) For equation $I$: $x^{2}-82x+781=0$.We need two numbers whose product is $781$ and sum is $82$. These numbers are $71$ and $11$.So,$(x-71)(x-11)=0$,which gives $x = 71$ or $x = 11$.For equation $II$: $y^{2}=5041$.Taking the square root on both sides,$y = \pm \sqrt{5041} = \pm 71$.So,$y = 71$ or $y = -71$.Comparing the values:If $x = 71$ and $y = 71$,then $x = y$.If $x = 71$ and $y = -71$,then $x > y$.If $x = 11$ and $y = 71$,then $x Since we get different relationships ($x = y$,$x > y$,and $x < y$) depending on the values chosen,the relationship between $x$ and $y$ cannot be established.

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-82x+781=0$
$II.$ $y^{2}=5041$

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Solve the given two equations and select the correct answer from the given options.$I.$ $x^{2}-82x+781=0$$II.$ $y^{2}=5041$