If a^2 + b^2 = ( a+b)^2 . Find all possible pairs of numbers a and b.

a^2 + b^2 = ( a+ b) ^2

Let us
simplify the expression.

We know
that:

(a+ b)^2 = a^2 + 2ab +
b^2

We will substitute into the equation
above.

==> a^2 + b^2 = a^2 + 2ab +
b^2

Now we will subtract a^2 and b^2 from both
sides:

==> a^2 + b^2 - a^2 - b^2 = a^2 + 2ab+ b^2 -
a^2 - b^2

==> 0 =
2ab

==> 2ab =
0

==> a*b = 0

Then, we
conclude that in order for the equality to hole, either a or b should equal
zero.

Then: a = 0   OR   b =
0

Then there are unlimited possible solutions
for the equality such that the pair ( a,b)
is:

(a,b) = { ( a, 0) : a is
any real
number}.

          ={( 0, b) :
b is any real number}.