document.write( "Question 737616: Give a counterexample to show that (x+y)2 = x2 + y2 is false. \n" ); document.write( "

Algebra.Com's Answer #450457 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "To find a counter example to \" $\"%28x%2B+y%29%5E2\"$ is $\"NOT\"$ $\"x%5E2%2B+y%5E2\"$ \", you must use $\"x\"$ and $\"y\"$ so that $\"%28x%2By%29%5E2=+x%5E2%2B+y%5E2\"$ .\r
\n" ); document.write( "\n" ); document.write( "Presumably you know that $\"%28x%2B+y%29%5E2=+x%5E2%2B+2xy%2B+y%5E2\"$ . That means you must find $\"x\"$ and $\"y\"$ so that $\"x%5E2%2B+2xy%2B+y%5E2=+x%5E2%2B+y%5E2\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"cross%28x%5E2%29%2B+2xy%2B+cross%28y%5E2%29=+cross%28x%5E2%29%2B+cross%28y%5E2%29\"$ ...notice that the squares on both sides cancel\r
\n" ); document.write( "\n" ); document.write( " What does that leave you with? \r
\n" ); document.write( "\n" ); document.write( " $\"2xy=+0\"$ ...this is true only if only $\"x=0\"$ or $\"y=0\"$ , or both $\"x=0\"$ and $\"y=0\"$ \r
\n" ); document.write( "\n" ); document.write( "so, it proves that $\"%28x%2B+y%29%5E2%3C%3Ex%5E2%2B+y%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );