Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Can someone tell how to find this general rule

For a given equation

ax^3+cx=d

, to find x , it says use

u-v=d, uv=(c/3)^3

, and then

Unparseable latex formula:

x=\sqrt[3]{u}-\sqrt[3]{v}}

.

My question is how do I find this underlined part , :confused:

:confused:

??( the book does not mention it)

Solve
u-v=d
and
uv=(c/3)^3
simultaneously.

(For a given equation you will know c and d.)

OP

rnd

Solve
u-v=d
and
uv=(c/3)^3
simultaneously.

(For a given equation you will know c and d.)

My question is how do I deirive [ u-v=d , and uv = (c/3)^3,

Unparseable latex formula:

x=\sqrt[3]{u}-\sqrt[3]{v}}

}.

given only that

ax^3+cx=d

soory if my question isnt specific

Are you sure you want to derive those equations?

If you just want to solve them then you have u=d+v, sub that in uv=(c/3)^3 rarrange to get a quadratic equation and solve it to get v in terms of c and d.

But how can you not be using a?

OP

yes, I want to know how they found the equations(I think the bok assumes its obvious :rolleyes:

:rolleyes:

.I know how to find x using u and v.

rbnphlp

yes, I want to know how they found the equations(I think the bok assumes its obvious :rolleyes:

:rolleyes:

.I know how to find x using u and v.

OK. I'm giving up on this one then. Hope someone else helps you out. :smile:

:smile:

My point about a still stands though. How can x depend on c and d but not a? It can't. What's the book by the way?

It looks like the standard cubic solution equation in the special case where b=0 and a=1. There's a derivation of the solution on this page:

http://en.wikipedia.org/wiki/Cubic_equation#Roots_of_a_cubic_function

OP

rnd

OK. I'm giving up on this one then. Hope someone else helps you out. :smile:

:smile:

My point about a still stands though. How can x depend on c and d but not a? It can't. What's the book by the way?

History of mathematics :smile:

:smile:

quite intresting

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