Here's an example of an inconsistent equation:
3x/(x-2) = (4x2 - 8x)/(x2 - 4x + 4)
On its face, it looks perfectly fine. It is not immediately obvious that you can't solve for x and get a meaningful result. But if you take the time to factor the numerator and denominator of the righthand part of the equation, you'll start to see the problem. If you continue and try to solve for x using normal algebraic techniques, you will get the impossible result: 3 = 4.
That result shows that your starting equation is internally inconsistent; that is, it is not consistent with itself.
Solution:
3x/(x-2) = (4x2 - 8x)/(x2 - 4x + 4)
3x/(x-2) = 4x(x - 2)/(x - 2)2
3x = 4x
!!
Don't you like x=0?
As a solution to your full-consistent equation?
Beside that, your definition of self-consistent equation is right. On the contrary the specific example is not.
It is worth noting that often "self-consistent equation" is a misuse for "self-consistency equation", namely an equation whose role is to guarantee the self consistency of a theory (model, whatever). If the equation is satisfied then the theory is self-consistent.
Literally a "self-consistent equation" is a meaningful one.
Wiki User
∙ 14y agoWhen its matrix is non-singular.
Consistent means that the equation does not have the same slopes. Inconsistent means that it has the same slope.
yes it can . the system may have infinitely many solutions.
It is consistent with some equations, not with others.
The answer depends on consistent with WHAT!
Consistent equations are two or more equations that have the same solution.
It depends on the equations.
When its matrix is non-singular.
Consistent means that the equation does not have the same slopes. Inconsistent means that it has the same slope.
self-consistent belief and practice
That doesn't apply to "an" equation, but to a set of equations (2 or more). Two equations are:* Inconsistent, if they have no common solution (a set of values, for the variables, that satisfies ALL the equations in the set). * Consistent, if they do. * Dependent, if one equation can be derived from the others. In this case, this equation doesn't provide any extra information. As a simple example, one equation is the same as another equation, multiplying both sides by a constant. * Independent, if this is not the case.
A consistent system.
flour + oven = rise
Libertarian
yes it can . the system may have infinitely many solutions.
Richard Brownell True has written: 'Space-charge-limited beam forming systems analyzed by the method of self-consistent fields with solution of Poisson's equation on a deformable relaxation mesh' -- subject(s): Electron beams, Electron gun
Only if you have two years of tax returns to show somewhat consistent earnings.