What is the unsolvable equation?

Answer 1

Usually, when people talk about solvable equations, they are talking about taking a polynomial and setting it to zero & then finding all of the roots of the equation.

A linear equation (ax+b = 0) is easy to solve.

A quadratic equation (ax^2+bx+c = 0) is not so hard. You probably learned the quadratic equation in high school. That formula has been around since the ancient Greeks.

What about cubic equations? (ax^3+bx^2+cx+d = 0) It turns out that there is a formula that you can use to find the three roots of the equation. It was discovered in the 1300s by Tartaglia. It is a very complicated formula.

The obvious next choice is to see if we can solve fourth degree equations using a formula. Legendre discovered the formula for this in the late 18th century.

Then a few interesting things happened. Gauss had already proven that every polynomial with integral coefficients has a solution in the complex numbers. But in the early 1800s, Nicholas Abel proved that there is no general formula for solving equations of degree five or higher. Sure -- we know that some can be solved (x^5-32=0 has five roots that can be found, including 2). But there is no general formula.

A few years later, a young Frenchman named Evariste Galois created a beautiful system that allows us to take any polynomial and through a series of steps tells us exactly which polynomial equations can be solved and which ones cannot be solved. It took another 50 years for people to find out about his work, because he was killed in a duel before he turned 21.

So -- if you want to know if an equation is unsolvable, just use Galois' method.

Answer 2

the equation which has no solution. There are lots of unsolvable equation. Try solving: x^2 = -5

Answer 3

The ancient Greeks founded Western mathematics, but as ingenious as they were, they could not solve three problems:

1. Trisect an angle using only a straightedge and compass
2. Construct a cube with twice the volume of a given cube
3. Construct a square with the same area as a given circle

It was not until the 19th century that mathematicians showed that these problems could not be solved using the methods specified by the Greeks.

Any good draftsman can do all these constructions accurate to any desired limits of accuracy - but not to absolute accuracy.

The Greeks themselves invented ways to solve the first two exactly, using tools other than a straightedge and compass. But under the conditions the Greeks specified, the problems are impossible.

http://www.uwgb.edu/dutchs/PSEUDOSC/trisect.HTM

Answer 4

"THE" unsolvable equation?
There are infinitely many unsolvable equations.
This is provable.
Do you have one in mind?
Or do you just need one?

Answer 5

Actually meow isn't the answer to your equation the square root of 5i. Don't know how to do a square root symbol on a keyboard myself. But i * i = -1. It is an imanginary number.

Answer 6

can you sole it? x+y= 10 and 2x+2y= 23..this is unsolvable..

Answer 7

An equation that cannot be solved.

Answer 8

Everything, Infinite.

Answer 9

a^3+b^3=c^3 where a, b, and c are all non-zero integers.