anonymous
  • anonymous
Prove by contradiction. Suppose that x and y are positive integers. Show that the sq root of (x^2 + y^2) is not equal to x + y.
Mathematics
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chestercat
  • chestercat
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anonymous
  • anonymous
proof by contraction means suppose \[\sqrt{x^2+y^2}=x+y\]
anonymous
  • anonymous
then arrive at a contradiction, square both sides get \[x^2+y^2=(x+y)^2\]
anonymous
  • anonymous
so \[x^2+y^2=x^2+y^2+2xy\] \[0=2xy\] imples either \(x=0\) or \(y=0\)

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anonymous
  • anonymous
and since 0 is not a positive integer, this contracts the assumption that both x and y are positive integers

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