<p>I'm having trouble figuring out how to solve the following problem:</p>
<p>Question:</p>
<p>If x^2 + y^2 = 73 and xy = 24, what is the value of (x+y)^2?</p>
<p>Do you use the fact that xy=24 to divide by either x or y and substitute that back into the problem?</p>
<p>Fastest way imo is to see that xy=24 leaves a couple of options for the values. It’s either 1 and 24, 2 and 12, 3 and 8, or 4 and 6 for the values of x and y.</p>
<p>Next, since x^2 + y^2 = 73, it is clear that 3 and 8 is the only set of values that works.</p>
<p>Finally, (3+8)^2 = 121.</p>
<p>I think I figured it out:</p>
<p>(x+y)^2 = (x+y)(x+y) = x^2+xy+xy+y^2 = x^2+2xy+y^2</p>
<p>2xy + 73
2(24) + 73
48 + 73
121</p>
<p>Plugging in the different factors, like you suggested, seemed to work, too.</p>