The condition of one-dimensional linear equation without solution

One-dimensional linear equation has no solution if its root is irrational.

In a linear equation, if the root of the equation is an irrational number, that is, the root cannot be expressed as the ratio of two integers, then the equation has no solution. This is because the form of a linear equation is ax+b=0, where a and b are constants and x is unknown. When both a and b are rational numbers, the rational number solution can be obtained by solving. But when one or both of them are irrational numbers, there is no rational number solution, so the equation has no solution.

For example, the equation sqrt(2)+sqrt(3)=0 has no solution, because both sqrt(2) and sqrt(3) are irrational numbers, and no rational number can satisfy the equation. Similarly, if the equation is in the form of ax+b=c, where A, B and C are rational numbers, when C is not rational, the equation has no solution.

One-dimensional linear equation has no solution if its root is irrational. This is because irrational numbers cannot be expressed as the ratio of two integers, so it is impossible to find rational numbers that satisfy the equation.

The form of solution of one-dimensional linear equation;

The standard form of linear equation is ax+b=0, where a and b are constants and x is unknown. The form of the solution is x=(-b/a).

In the standard form, when a≠0, the equation has a unique solution, that is, x =-b/a; When a=0, the equation has no solution.

In addition, one-dimensional linear equations can have other forms, such as shifting terms, merging similar terms, removing brackets, removing denominator and so on. For these forms of equations, we can solve them according to different methods.

For example, for the equation 2x-7=3, we can first shift the terms to get 2x=3+7, then merge similar terms to get 2x= 10, and finally divide the two sides by 2 to get x=5.

The standard form of linear equation is ax+b=0, where a≠0. The form of the solution is x=(-b/a), but for the case of a=0, it needs to be analyzed according to specific problems. At the same time, the equation can have other forms and needs to be solved according to different methods.