Alan

HoldMyBeer's answers are correct:

Doing it numerically, using some software, I get the following, though I can't see a simple way of doing it by hand:

If the two equations have a common root you can equate them (the two equations) to find the two values of x for which it holds (the bx terms cancel out).

Substitute each value of x into either equation and solve for b.  

You should find two values (though not 17675308 or -17675308 according to my calculations).

These are usually best done by using polar coordinates. e.g.

Like so:

In these sort of questions it's often a good idea to plot a graph, then use Newton-Raphson iteration.

No!  The right-hand side of your first line should be -21 + 7x + 3x.

The correct answer is 6.

You should be able to recognise this as the difference of two squares:  a² - b² = (a+b)*(a-b)

Here, a = 10001 and b = 9999, so this is actually easy to calculate in your head.

"range" refers to the output.  "domain" refers to the input.

As follows: