Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Equation

Can anybody give a solution to this equation:

Pls give atleast a few values for this so that the equation is true!

Is it possible to do with real numbers or only possible with imaginary numbers? If only imaginary numbers are there, what are they?

Pls show how u did this also!

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation

Hi Agnishom;

Hi;

This can be rewritten as

Now a could be real and b imaginary. After those I think all the remaining have either a or b imaginary.

Had a hallucination on an earlier solution which I forgot to plug in. Found out it was not a solution at all. Got drowsy and fell asleep. What I wanted to say was if you look at the second equation you see that the LHS is always positive and the RHS is always negative. There just cannot be any real b that could do that.

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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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Equation

Can u please give a few solutions (even if in imaginary)?

Also show how you got that.

Thanks

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation

Hi;

To get some solutions you do the same thing you would do to get a solution of any any eqaution with 2 variables. You fix on variable and solve for the other.

Another way to write your problem is:

Set a = 2 and solve for b:

Can you solve for b? To get more solutions give more arbitrary values to a and solve for b.

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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.

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Equation

. .

.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Equation

hi Agnishom,

Is it possible to do with real numbers or only possible with imaginary numbers?

Working on from soroban's equation:

if you divide by b squared (ok since it will not be zero from the original equation)

Now replace a/b by x

which has complex solutions.

Thus if 'a' is chosen to be real, 'b' must be complex and vice versa.

They may also both be complex.

So, in summary, a and b can never both be real.

Bob

Last edited by Bob (2011-03-11 06:01:48)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Equation

Thanks

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.