Question

Find counter examples to disprove the following statement.
For any integers x and y, $\sqrt{x^2+y^2}=x+y$.

Answer 1

The x and y are , $\sqrt{x^2+y^2}=x+y$

for x=3, y=4 ,and x=4 and y=5

Then $\sqrt{3^2+4^2}\ne 3+4$

And $\sqrt{4^2+5^2}\ne 4+5$

Then disprove the statement $\sqrt{x^2+y^2}=x+y$

But x=0 and y=1 and x=0 and y=0

$\sqrt{0^2+1^2}=0+1$

$\sqrt{0^2+0^2}=0+0$

It is prove