Math Is Fun Forum

DaveRobinsonUK1

Member

Registered: 2011-12-01

Posts: 12

Dual Variable Quadratic Solve

Hi Guys

I have a problem, I have spent so long (the last year or so) working on differentiating and integrating multivariable stuff that I have completely bypassed just being able to solve them. And now I need to be able to solve them. Bummer. I've had a go at the problem I have, though came unstuck and when I did some reading on the tinterweb its all confusing.

Here is the problem.

supposed to solve for r with the results given as

or

the closest i have come has been

All i have done to go further than this just doesn't go anywhere into being a
quadratic that I could solve.

---

I see it, but I don't believe it.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Dual Variable Quadratic Solve

Hi DaveRobinsonUK1;

How are you?

Expand out both sides:

Subtract the RHS from the LHS and you get:

Factor:

Can you take it from there?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DaveRobinsonUK1

Member

Registered: 2011-12-01

Posts: 12

Re: Dual Variable Quadratic Solve

Hi Bobby

Thanks for this.

I can follow it to there, and then i got this. Not sure if its cheating or not.

if i divide by

and then mult by -1 i get

and

if I divide by

i can get

which would be

i have done this by assuming that the rhs contains the empty set. Though I'm not sure
if that is valid.

---

I see it, but I don't believe it.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Dual Variable Quadratic Solve

Hi;

It is not necessary to divide like that.

Set both factors equal to 0 and solve:

The first one is obviously r = 0. Please solve for r in the second one and post what you get.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DaveRobinsonUK1

Member

Registered: 2011-12-01

Posts: 12

Re: Dual Variable Quadratic Solve

Hi Bobby

Sorry about the delay, been a hectic week here.

---

I see it, but I don't believe it.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Dual Variable Quadratic Solve

Hi DaveRobinsonUK1;

That is correct!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DaveRobinsonUK1

Member

Registered: 2011-12-01

Posts: 12

Re: Dual Variable Quadratic Solve

cool my man!

I can move on with this Universal Hyperbolic stuff now. Apparently .

---

I see it, but I don't believe it.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Dual Variable Quadratic Solve

Hi DaveRobinsonUK1;

Good luck! Watch out for those hyperbolics they can be dangerous.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.