Given the law of composition xy 2xy 6x 6y 21 solve the e

Given the law of composition x*y = 2xy - 6x - 6y + 21 solve the equation x*x*x = 3

Solution

We\'ll re-write the law of composition as:

2xy - 6x - 6y + 21 = 2(x-3)(y-3) + 3

Now, we\'ll apply the law of composition for x*x:

x*x = 2(x-3)(x-3) + 3

x*x = 2(x-3)^2 + 3

Now we\'ll solve x*x*x:

[2(x-3)^2 + 3]*x = 2[2(x-3)^2 + 3 - 3](x-3) + 3

We\'ll eliminate like terms:

4(x-3)^3 + 3 = 3

We\'ll eliminate like terms:

4(x-3)^3 = 0

We\'ll divide by 4:

(x-3)^3 = 0

The solutions of the equation are: x1 = x2 = x3 = 3.