Question 1095268
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How much x square -y square ? if x+y=66 xy=9
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Tutor @greenestamps provided the answer   {{{x^2-y^2}}} = {{{792sqrt(30)}}}.


This answer is correct,  but incomplete.


This problem has a symmetry &nbsp;(x.y) <---> (y,x).


In other words, values x and y can be rearranged.


It means that together with the answer &nbsp;{{{x^2-y^2}}} = {{{792sqrt(30)}}}
&nbsp;another answer &nbsp;{{{x^2-y^2}}} = {{{-792sqrt(30)}}} &nbsp;is valid and is possible, &nbsp;too.


So, the complete answer to the problem is THIS:


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- under given conditions, &nbsp;{{{x^2-y^2}}} &nbsp;may have two different values.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;One possible value is &nbsp;{{{792sqrt(30)}}}; &nbsp;another possible value is &nbsp;{{{-792sqrt(30)}}}.