SOLUTION: I need to say what is wrong with this statement: {{{ sqrt(x^2+y^2) = x+y }}} Would it be that it should be = {{{ x^2+y^2 }}} ? Thanks for the help!

Algebra ->  Square-cubic-other-roots -> SOLUTION: I need to say what is wrong with this statement: {{{ sqrt(x^2+y^2) = x+y }}} Would it be that it should be = {{{ x^2+y^2 }}} ? Thanks for the help!      Log On


   

Question 335286: I need to say what is wrong with this statement:
+sqrt%28x%5E2%2By%5E2%29+=+x%2By+
Would it be that it should be = +x%5E2%2By%5E2+ ?
Thanks for the help!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Square both sides.
x%5E2%2By%5E2=%28x%2By%29%5E2
x%5E2%2By%5E2=%28x%2By%29%28x%2By%29
x%5E2%2By%5E2=x%5E2%2Bxy%2Byx%2By%5E2
x%5E2%2By%5E2=x%5E2%2B2xy%2By%5E2
2xy=0
So the above equality only holds if either x or y or both are zero.
Otherwise you're missing the 2xy term.
sqrt%28x%5E2%2B2xy%2By%5E2%29=sqrt%28%28x%2By%29%5E2%29=x%2By