Math Is Fun Forum

aimarito

Guest

solve this

get the value of x and y ?!

( x - 1 ) ( y  ² + 6 ) = y ( x  ² + 1 )
( y - 1 ) ( x  ² + 6 ) = x ( y  ² + 1 )

aimarito

Guest

Re: solve this

anybody ?

lightning

Real Member

Registered: 2007-02-26

Posts: 2,060

Re: solve this

sorry i don't know

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Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: solve this

It's a group of Equation or just two separate equations?

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Numbers are the essence of the Universe

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: solve this

Simultaneous non-linear equations in x and y, I believe.

Here’s a hint: Notice that the second equation is exactly the same as the first with x and y interchanged? Therefore one possibility is x = y. Try putting that into one of the equations and see what happens.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: solve this

Hi;

Form the Sylvester Matrix:

Take the determinant of that matrix, best done with a CAS.

Form the new equation to solve. This equation will have the same roots as the above 2 equations. This is a standard way to reduce the number of variables.

By the Descartes rule of signs there are 0,2,4 or 6 positive real roots. Plotting the polynomial:

http://www.mathsisfun.com/graph/functio … ymax=5.106

We see roots of 2 and 3, we verify them by plugging into the polynomial.

We deflate out the roots of 2 and 3.

Descartes says 0,2 or 4 positive real roots. Using the rational root theorem these are the possible rational roots that are positive.

We find two and three again by plugging in and deflate out again.

Use the quadratic formula:

So we have for roots by plugging in the original polynomials.

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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.