Solve the qubic x^3 - 7x + 6 using Cardano's Method. Express all your
answers as possible irrational numbers (i.e. no decimals!) and show your steps.
Please help---this problem is driving me nuts!
I haven't done this in a while but this may help
Cardano's Method
I'll see if I can work out a step or two to get you started.
It looks like your teacher or textbook already did the first step for you, eliminating the square term by the substitution
y = x + (b/3)a
I'll add to the number of ways to solve this. See this page. I usually use what's called "Vieta's Substitution." (A bit down the page.) And the trigonometric method (further down the page) has its points as well, though it's a bit more complicated. This is really nice if you need to show how many real roots the cubic has.
-Dan