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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^{2}-71x-11x+7

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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^{2}-71x-11x+781=0$$x(x-71)-11(x-71)=0$$(x-71)(x-11)=0$Therefore,$x = 71$ or $x = 11$.For equation $II$: $y^{2}-5041=0$$y^{2} = 5041$$y = \pm \sqrt{5041}$$y = 71$ or $y = -71$.Comparing the values:If $x = 71$,then $x = y$ (when $y=71$) and $x > y$ (when $y=-71$).If $x = 11$,then $x  y$ (when $y=-71$).Since the relationship varies depending on the values chosen,the relationship between $x$ and $y$ cannot be established.

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

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