<p>If x^2 + y^2 = 73 and xy = 24, what is the value of (x+y)^2</p>
<p>a - 73
b - 97
c- 100
d - 121
e - 144</p>
<p>correct answer = d, 121</p>
<p>now, the way i did it was like guess and check i tried 6 and 4 first being factors of 24, then i tried 8 and 3 and got it, is there any other efficient way of solving this?</p>
<p>Use the fact that (x+y)^2 = x^2 + y^2 + 2*xy …</p>
<p>Look at the right hand side, and compare with the information you are given…</p>
<p>If x^2 + y^2 = 73 and xy = 24, what is the value of (x+y)^2</p>
<p>a - 73
b - 97
c- 100
d - 121
e - 144</p>
<p>(x+y)^2 = x^2 + 2xy + y^2
= (x^2 + y^2) + 2(xy)
= (73) + 2(24)
= 121</p>
<p>This is a very common problem, so remember this method. You don’t have to do it in as many steps as I did, but I just did it that way for clarity.</p>
<p>But the quickest way is the way DoctaJ did it…</p>
<p>Also, this is a blue book problem, test#1…you could check the BB thread or Khan academy…</p>
<p>Not necessarily. </p>
<p>First his method requires to find the factors of 24. Then you have to see if the square of two of those factors = 73. After all that, you have to add them together and then square the sum.</p>
<p>or you could do
x^2 + 2xy + y^2
73 + 2(24)
= 121</p>
<p>Takes all of 10 seconds.</p>