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

(i)

Given that $\displaystyle cx = \sqrt{\frac{ax^2 - b}{d}}$ express x in terms of a,b,c & d.

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

(ii)

If $\displaystyle x = p + \sqrt{q} $ where p and q are rational, show that $\displaystyle x^2$ and [tex]x^3/math] are of the form $\displaystyle P + Q\sqrt{q}$ where P and Q are rational.

I'm stuck on this one completely

(iii)

Verify that $\displaystyle z = (4+\sqrt{15})^\frac{1}{3} + (4-\sqrt{15})^\frac{1}{3}$ satisfies $\displaystyle z^3 -3z +8 =0$

Not sure what is ment here...

(iv)

Given that $\displaystyle \alpha$ and $\displaystyle \beta$ are roots of the equation $\displaystyle x^2 + 3x -6 =0$ find a quadratic equation with integer coefficiants whose roots are $\displaystyle \frac{2}{\alpha}$ and $\displaystyle \frac{2}{\beta}$

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