SOLUTION: if x-y=7, xy=-8, what is the value of x^2+3xy+y^2

Algebra ->  Square-cubic-other-roots -> SOLUTION: if x-y=7, xy=-8, what is the value of x^2+3xy+y^2      Log On


   

Question 892936: if x-y=7, xy=-8, what is the value of x^2+3xy+y^2
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x-y=7%2C+xy=-8%29

Square both sides of

x-y=7

x%5E2-2xy%2By%5E2=49

Add 5xy to both sides:

x%5E2%2B3xy%2By%5E2=49%2B5xy

Since xy=-8, substitute -8 for xy on the right:

x%5E2%2B3xy%2By%5E2=49%2B5%28-8%29

x%5E2%2B3xy%2By%5E2=49-40

x%5E2%2B3xy%2By%5E2=9

Edwin