Given the law of composition xoy=x+y+xy solve the equation (x^2-5)o3=-1.

To solve the equation, we'll have to use the given law of
composition and to replace x and y by the terms (x^2 - 5) and
3.

(x^2 - 5)o3 = (x^2 - 5) + 3 + 3x^2 -
15

But (x^2 - 5)o3 = -1 => (x^2 - 5) + 3 + 3x^2 - 15
= -1

We'll remove the brackets and we'll shift all terms to
one side:

x^2 - 5 + 3 + 3x^2 - 15 + 1 =
0

We'll combine like
terms:

4x^2 - 16 = 0

We'll
divide by 4:

x^2 - 4 = 0

x^2 =
4 => x1 = 2 and x2 = -2

The solutions
of the equation are {-2 ; 2}.