Question 607958
{{{y=(a+b)^2}}}
To better understand the solution to this, let's go ahead and multiply out the right side:
{{{y=a^2+2ab+b^2}}}<br>
So we are supposed to figure out y from ab=10 and {{{a^2+b^2=30}}}. If we multiply both sides of ab=10 by 2 we can get a value for the middle term of {{{a^2+2ab+b^2}}}:
2ab = 20
Now if we add that equation to the other one we match the full expression:
{{{a^2+b^2 = 30}}}
+
{{{2ab = 20}}}
____________
{{{a^2 + 2ab + b^2 = 50}}}
So y equals 50! (And we know this without ever knowing what "a" or "b" are!)