Sqrt of number equal to the same number, but not 0 or 1???

Question

Please solve :

sqrt(x) = x , but x is not equal to either 0 or 1?

I know of two other numbers besides 0 and 1 which satisfy this equation! So lets see if there are any boffs out there!

Answer 1

Infinite

Answer 2

Even in the Complex Numbers, zero and one are the only solutions. The Fundamental Theorem of Algebra (first proved by a 19 year old Gauss as his Doctoral Dissertation) states that any n'th degree polynomial with integral coefficients has at most N roots in the complex plane. That means that a quadratic equation caqnhave at most two roots. You have already found both of them.

Now if you want to look at other sistems -- like Hamilton's Quaternions, we can find more solutions.

Answer 3

Actually, it can be a complex number but it is no real other than 0 or 1, even infinity(by limits). We can have a complex number because no purely imaginary number is allowed as a logarithm base.

Answer 4

This is a second degree equation in x (a polynomial, not a sine for instance) 2 solutions are all you get.

Answer 5

not possible. the roots are 0 and 1 only. are you dumb freak?

Answer 6

it can be solved as we solve quadratic equations
sqt(x)=x
or x2-x=0
x(x-1)=0
either x==1 or 0
no other answer is possible

Answer 7

y^2=y now when u can figure out y ill tell u x