<p>Help me solve:
If ab=36 and a^2+b^2=97, then (a+b)^2</p>
<p>I'm trying to help my daughter and I need all the help I can get myself.
Thanks</p>
<p>Answer should be 169.</p>
<p>You know there are only so many pairs of integers that have a product of 36. (36, 1), (18,2), (9,4), (3,12). </p>
<p>So what I did was just plug in these possibilities into the second equation and I saw that 9^2 + 4^2 = 97</p>
<p>Then I added 9+4 = 13 (just in case you didn't know)</p>
<p>13^2 = 169</p>
<p>You make it look easy - I greatly appreciate the help</p>
<p>I got the same answer with a different method:</p>
<p>a² + 2ab + b² = ?
we are told a² + b² = 97
So we can substitute that and get 97 +2ab = ?
Now, we know that ab = 36, so 2(36) = 72
97 + 72 = 169
Quick, and efficient.
Hope that helped.</p>
<p>yup... so many ways to do all these sat problems</p>