Yes, some equations are unsolvable, meaning that there is no way to find a solution or answer for them. An example of an unsolvable equation is x² + 1 = 0.
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Yes, some equations are indeed unsolvable. This means that there is no way to find a solution or answer for them. An unsolvable equation is one that cannot be solved by using algebraic methods. According to MathIsFun, “no general formula exists for solving equations of degree five or higher using radicals.” These are known as “unsolvable quintic equations”.
One of the most famous unsolvable equations is the aforementioned x² + 1 = 0. This equation has no real solution because the square of any real number is always positive. As a math teacher once said, “it’s as if you’re asking for a number that when you square it, it becomes negative. That just doesn’t exist in the realm of real numbers.”
In fact, there are many unsolvable equations in math. Some of them are so complex that even mathematicians spend years trying to figure them out. One such example is Fermat’s Last Theorem, which stated that there are no three integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. This theorem was famously unsolvable for hundreds of years until it was finally proved by Andrew Wiles in 1994.
Another interesting fact is that sometimes equations can be solved by using a combination of algebraic and numerical methods. For instance, the equation x + e^x = 0 cannot be solved by any algebraic method, but it can be solved numerically using a computer program.
In conclusion, there are many unsolvable equations in math, and while they may seem frustrating, they also highlight the incredible complexity and beauty of mathematics. As famous mathematician Henri Poincaré once said, “Mathematics is the art of giving the same name to different things.”
| Equation | Solvable? |
|---|---|
| x² + 1 = 0 | No |
| a^n + b^n = c^n (n > 2) | No |
| x + e^x = 0 | Yes, with numerical methods |
Further answers can be found here
Some equations have no solutions, others have plenty! Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
After 10 years, Prof. Raimar Wulkenhaar from the University of Münster’s Mathematical Institute and his colleague Dr. Erik Panzer from the University of Oxford have solved a mathematical equation which was considered to be unsolvable. The equation is to be used to find answers to questions posed by elementary particle physics.
Like the rest of us, you’re probably expecting some next-level difficulty in these mathematical problems. Surprisingly, that is not the case. Some of these equations are even based on elementary school concepts and are easily understandable – just unsolvable.
There are plenty of mathematical expressions that have no exact solution. Take one of the most famous numbers ever, pi, which is the ratio of a circle’s circumference to its diameter. Proving that it was impossible for pi’s digits after the decimal point to ever end was one of the greatest contributions to maths.
A2A, thanks.
No, it’s worse than that. Kurt Godel has proved that, roughly speaking, among the statements generated by a system of logic, there will necessarily be statements that can’t be verified (within that system) as true or false. See godel’s incompleteness theorems – Google Search [ https://www.google.com/search?sxsrf=ALeKk00V7dybhKQAPq4H8eUY86cCfEyYxg%3A1586103758088&ei=zgWKXpnxBN680PEP-5SC2AE&q=godel%27s+incompleteness+theorems&oq=godel%27s+incompleteness+theorems&gs_lcp=CgZwc3ktYWIQAzIHCAAQFBCHAjICCAAyBggAEBYQHjIGCAAQFhAeMgYIABAWEB4yBggAEBYQHjIGCAAQFhAeMggIABAWEAoQHjIGCAAQFhAeMgYIABAWEB46BAgAEEdKCQgXEgUxMi00MUoICBgSBDEyLTNQjDRYjDRgnDloAHACeACAAUmIAUmSAQExmAEAoAEBqgEHZ3dzLXdpeg&sclient=psy-ab&ved=0ahUKEwiZkM_42NHoAhVeHjQIHXuKABsQ4dUDCAw&uact=5 ]. Such statements are sometimes called undecidable propositions.
I suppose, the “variables” that are missing are those our human cognitive apparatus cannot fathom because of its inherent limitations.
Perhaps a simpler example of how …
This video has the solution to your question
The Collatz Conjecture is a problem in mathematics that is said to be incredibly difficult to solve. The problem involves determining whether or not a set of positive integers will eventually end up in a loop created by applying two rules. Professional mathematicians have been unable to solve the problem, but Jeffrey Lagarias is the world authority on the conjecture.
More interesting questions on the issue
Beside above, Are there unsolvable equations? The answer is: The Euler-Mascheroni Constant
The character y is what is known as the Euler-Mascheroni constant and it has a value of 0.5772. This equation has been calculated up to almost half of a trillion digits and yet no one has been able to tell if it is a rational number or not.
Consequently, How do you know if an equation is unsolvable? As an answer to this: If your vector b (which consists of all the entries to the RIGHT of the equals sign) is not in the column space of A (which is a matrix consisting of all of the coefficients of x, y, and z in this example), the system is unsolvable.
Also Know, What equation Cannot be solved?
Answer will be: These are called transcendental equations. When you have a polynomial equation that you cannot solve, then you say that the equation "is not solvable by radicals."
What are the 7 unsolved maths problems? Response will be: Clay “to increase and disseminate mathematical knowledge.” The seven problems, which were announced in 2000, are the Riemann hypothesis, P versus NP problem, Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier-Stokes equation, Yang-Mills theory, and Poincaré conjecture.
Also, What are the 7 unsolvable math problems? What are the 7 unsolved problems? The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.
Also Know, What are the 7 unsolved math problems? Answer to this: What are the 7 unsolvable math problems? The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.
Then, What is the world’s hardest math equation? The response is: The Navier-Stokes equation, for me is the hardest of all. This is the full Navier-Stokes equation in conservative form. It looks pretty simple, but as one will dig in, they will notice why it is the hardest one.
What are the 7 unsolvable math problems?
What are the 7 unsolved problems? The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.
In this way, What are the 7 unsolved math problems? What are the 7 unsolvable math problems? The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.
Accordingly, What is the world’s hardest math equation?
Response will be: The Navier-Stokes equation, for me is the hardest of all. This is the full Navier-Stokes equation in conservative form. It looks pretty simple, but as one will dig in, they will notice why it is the hardest one.