Posted by Subhotosh Khan on October 26, 2002 at 12:50:57:
In Reply to: question.... posted by Denis Borris on October 26, 2002 at 00:03:00:
: x^4 - x^3 + 18x^2 - 16x + 96 = 0
: Say I got that equation; before solving it, I go:
: let k = x^4 - x^3; then:
: 18x^2 - 16x + 96 + k = 0 ; quadratic:
: 36x = 16 +- sqrt(-6656 - 72k)
: Because x^4 - x^3 can't be negative, can I tell whoever that
: equation belongs to to stick it up his/her sigmoid flexure ?
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This is a legitimate way of solving Diophantine (sp?) equations - where one seeks ONLY POSITVE INTEGER solutions. Then trial and error (or iterative)method can be set up for solution.
However, 99.99% of USEFUL equations do nat have real & rational solutions - let alone integer. Chances of finding that sigmoid flexure is less than 0.01% - that's why probably moon doesn't shine there......