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Topic: too many solutions (Read 2787 times) |
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Robert Grimsley
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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.
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towr
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Re: too many solutions
« Reply #1 on: Jun 10th, 2003, 1:59pm » |
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Just subtract 1 from each side, and it doesn't make a difference..
there's a thread on the problem somewhere allready btw..
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| « Last Edit: Jun 10th, 2003, 2:00pm by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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Icarus
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Re: too many solutions
« Reply #2 on: Jun 10th, 2003, 4:38pm » |
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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!
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TenaliRaman
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Re: too many solutions
« Reply #3 on: Jun 12th, 2003, 9:12am » |
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i think the same hint which was given to mystery triangle should be given to this one too.
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Pradeep Sekar
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Basic algebra reduces this to a ...
1 = 1 (Hey where did the X go?)
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Math sutdent
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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. 
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BNC
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Re: too many solutions
« Reply #6 on: Aug 25th, 2003, 12:55pm » |
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on Aug 25th, 2003, 6:48am, 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. |
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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.
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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