Thread: A few algebraic arithmetic questions that I'm stuck on....

Any help would be greatly appreciated I'm stuck on about 7 out of 30 questions - Here are a few:

(i)
Given that express x in terms of a,b,c & d.

Is this just a rearranging as I get a negative in my sqrt?

(ii)
If where p and q are rational, show that and [tex]x^3/math] are of the form where P and Q are rational.

I'm stuck on this one completely

(iii)
Verify that satisfies

Not sure what is ment here...

(iv)
Given that and are roots of the equation find a quadratic equation with integer coefficiants whose roots are and

I'm stuck with this and cannot find any examples of this online or in my text books.

Positive is that I've gotten to grips with LaTex

Thanks, Dojo

For (i), the first thing you'll want to do is square both sides of the equation. Then you need to isolate x on one side of the equation. It pretty much is a rearranging.

For (ii), just multiply out [Math](p + \sqrt{q})(p + \sqrt{q})[/tex] and note that a product or sum of rational numbers is rational.

Originally Posted by dojo

(iii)
Verify that satisfies

Not sure what is ment here...

This means if you expand



then simplify you should get zero.

Or just solve

What are the solutions??