SOLUTION: If ab=10 and {{{a^2 + b^2 = 30}}}, then solve for y in {{{y=(a+b)^2}}}.

Algebra ->  Expressions-with-variables -> SOLUTION: If ab=10 and {{{a^2 + b^2 = 30}}}, then solve for y in {{{y=(a+b)^2}}}.      Log On


   

Question 607958: If ab=10 and a%5E2+%2B+b%5E2+=+30, then solve for y in y=%28a%2Bb%29%5E2.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28a%2Bb%29%5E2
To better understand the solution to this, let's go ahead and multiply out the right side:
y=a%5E2%2B2ab%2Bb%5E2

So we are supposed to figure out y from ab=10 and a%5E2%2Bb%5E2=30. If we multiply both sides of ab=10 by 2 we can get a value for the middle term of a%5E2%2B2ab%2Bb%5E2:
2ab = 20
Now if we add that equation to the other one we match the full expression:
a%5E2%2Bb%5E2+=+30
+
2ab+=+20
____________
a%5E2+%2B+2ab+%2B+b%5E2+=+50
So y equals 50! (And we know this without ever knowing what "a" or "b" are!)