# Thread: sqrt (a^2 + b^2) = a + b

1. ## sqrt (a^2 + b^2) = a + b

What are all the a,b values that make this expression true expression:
sqrt(a^2 + b^2) = a + b

?

2. ## Re: sqrt (a^2 + b^2) = a + b

$\sqrt{a^2 + b^2} = a+b$

$a^2 + b^2 = a^2 + 2ab + b^2$

$0=2ab$

so either $a=0$, or $b=0$, or both.

3. ## Re: sqrt (a^2 + b^2) = a + b

Originally Posted by romsek
$\sqrt{a^2 + b^2} = a+b$
$a^2 + b^2 = a^2 + 2ab + b^2$
$0=2ab$
so either $a=0$, or $b=0$, or both.
Here is a counter-example.
Suppose $a=0~\&~b=-2$ then $\sqrt{0^2+(-2)^2}\ne 0+(-2)=-2$

4. ## Re: sqrt (a^2 + b^2) = a + b

Originally Posted by Plato
Here is a counter-example.
Suppose $a=0~\&~b=-2$ then $\sqrt{0^2+(-2)^2}\ne 0+(-2)=-2$
virtually anyone else on the forum would have simply replied

"you need to include $a,b \geq 0$"

but not you. No you have to provide a "counter-example" to show I'm wrong w/o actually helping the original poster any. Well done Plato, well done.

5. ## Re: sqrt (a^2 + b^2) = a + b

Originally Posted by romsek
virtually anyone else on the forum would have simply replied
"you need to include $a,b \geq 0$" but not you. No you have to provide a "counter-example" to show I'm wrong w/o actually helping the original poster any. Well done Plato, well done.
virtually??? In understand not everyone thinks like a mathematician.

P.S. as an after-thought. Given the history of the original poster, I very much was addressing him/her.

6. ## Re: sqrt (a^2 + b^2) = a + b

Originally Posted by romsek
> > > virtually anyone else < < < on the forum would have simply replied

"you need to include $a,b \geq 0$"
You're presumptuous. I'm fluent in elementary to intermediate algebra, and I missed what Plato pointed out (for the moment).

but not you. No you have to provide a "counter-example" to show I'm wrong w/o actually helping the original poster any. Well done Plato, well done.
This was simply an opportunity for you to post to Plato instead "Thank you, I did not clarify and/or emphasize that point you made for the student,
together with what I already showed."

7. ## Re: sqrt (a^2 + b^2) = a + b

Another solution:
Can I suppose a,b be complex numbers?