What is an equation that has no solution is called and 8203?

Answer 1

It is called an equation with no solutions in the domain under consideration. It is quite possible that an equation which does not have a solution in one domain has a simple solution in another - possibly broader - domain.

For example,

• a junior school pupil may tell you that x + 3 = 2 has no solution. In the domain of positive integers it does not but perhaps a year later, they will tell you that the answer is x = -1.
• a little later they may tell you that 3*x = 2 has no solution in the domain of integers. True, but in the domain of rational numbers, the answer is x = 2/3.
• Next, x2 = 2 has no solution in rational numbers but x = sqrt(2), is a perfectly valid solution in the domain of real numbers (which includes Irrational Numbers).
• Still further, x2 = -9 has no solution in real numbers since we all know that 32 = +9 and (-3)2 = +9. However, in the domain of imaginary numbers, x = 3i.
• and so on.

Also, there are equations which cannot be solved analytically, but do have solutions which can be found by numerical methods.