Question 1158710
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Let the numbers be x and y.  Then the given information is<br>
{{{x^2-y^2 = 21}}}
{{{3x^2+y^2 = 79}}}<br>
It should be obvious what method to use to solve the pair of equations; adding the two equations eliminates y.<br>
{{{4x^2 = 100}}}
{{{x^2 = 25}}}
{{{25-y^2 = 21}}}
{{{y^2 = 4}}}<br>
We know the square of one of the numbers is 25; but there is no information that lets us determine whether the number is 5 or -5.<br>
Likewise, we know the square of the other number is 4; but we can't tell if that number is 2 or -2.<br>
So we can only say that the two numbers are 5 or -5, and 2 or -2.<br>