wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> easy >> too many solutions
        
(Message started by: Robert Grimsley on Jun 10^th, 2003, 1:51pm)

Title: too many solutions
Post by Robert Grimsley on Jun 10^th, 2003, 1:51pm

I am 25 years out of school (and out of math), but is this a quadratic equation? I thought they had to equal zero, not one.

Title: Re: too many solutions
Post by towr on Jun 10^th, 2003, 1:59pm

Just subtract 1 from each side, and it doesn't make a difference..

there's a thread on the problem somewhere (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1043868251) allready btw..

Title: Re: too many solutions
Post by Icarus on Jun 10^th, 2003, 4:38pm

An equation is quadratic if it can be transformed into one of the form Ax²+Bx+C = 0. An equation such as Ax²+Bx+D = 1 is quadratic because it is equivalent to Ax²+Bx+(D-1) = 0.
As a general rule, if an equation
(1) involves no operations or functions other +,-,*,/ and integer exponents, and
(2) never divides by a variable expression, and
(3) in every term of the equation, if you multiply together the highest powers of x that would be multiplied in simplifying the term, you never get a result with exponent greater than 2,
then the equation is quadratic.

This is certainly the case here. Each term involves a highest power product of x*x (or of 1 on the right side of the equation), the denominators are all constant, and the only operations are the standard ones.

But...you have to be careful not to assume more than "quadratic" actually tells you!

Title: Re: too many solutions
Post by TenaliRaman on Jun 12^th, 2003, 9:12am

i think the same hint which was given to mystery triangle should be given to this one too.

Title: Re: too many solutions
Post by Pradeep Sekar on Aug 13^th, 2003, 4:38am

Basic algebra reduces this to a ...

1 = 1 (Hey where did the X go?)

Title: Re: too many solutions
Post by Math sutdent on Aug 25^th, 2003, 6:48am

Nice question. Notice x=0 dont solve the equation.
Multiply both sides of the equation by "x".
The equation is of degree 3 that is it
contain X^3. End of proof. :)

Title: Re: too many solutions
Post by BNC on Aug 25^th, 2003, 12:55pm

on 08/25/03 at 06:48:43, Math sutdent wrote:

Nice question. Notice x=0 dont solve the equation.
Multiply both sides of the equation by "x".
The equation is of degree 3 that is it
contain X^3. End of proof. :)

Defenitly not a third-degree equation.

In any case, multiplying both sides by X to add 1 to the degree of an equation is... well... strange practice.