1. ## Equation in R×R

Solve in R×R this equation :

2. Originally Posted by dhiab
Solve in R×R this equation :

real numbers x real numbers ?

3. Originally Posted by dhiab
Solve in R×R this equation :
$\displaystyle R \times R$ is, technically, the set of ordered pairs of real numbers which have no multiplication or addition defined on them. I thought you meant the vector space $\displaystyle R^2$. But in that case $\displaystyle \sqrt{a^2+ b^2}$ is a number while a+ b is a vector. Please explain what you mean by this question.

Are you asking for two real numbers, a and b, such that $\displaystyle \sqrt{a^2+ b^2}= a+ b$? In that case, a any non-negative real number and b= 0 is a solution.

real numbers x real numbers ?
Hello : FIND (a,b) a and b reals numbers.

5. Originally Posted by dhiab
Hello : FIND (a,b) a and b reals numbers.

ok .

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

$\displaystyle 2ab=0$

ab=0 .. then this is pretty obvious , one of it must be 0 .

Either a belongs to $\displaystyle R^+$, b=0 or the other way round .

6. thank you for the details solutions.

$\displaystyle a^2+b^2=a^2+2ab+b^2$
$\displaystyle 2ab=0$
Either a belongs to $\displaystyle R^+$, b=0 or the other way round .