What number is one more than the reciprocal of itself?

The two numbers that geno has generated are known as 'Phi".....and it's reciprocal, known as "phi"

And Phi has the property that it is 1 greater than phi

[ Phi = about 1.618       phi  = .618   ....!!!    ]

Note that the decimal part of Phi  = phi.......quite amazing....!!!

dad 123456

If the number is x, then the reciprocal will be 1/x and the equation is:  x  =  1 + 1/x

Multiplying both sides by x:  x²  =  x + 1

Rearranging:                       x² - x - 1  =  0

Using the quadratic fromula with  a = 1  b = -1  and  c = -1:

--->   x  =  [1 ±√(1+4)] / 2   --->   (1 ±√5)/2