Its Just A Fact Of Life

[aquamote]

1 + X = X (squared)

X=?

Just think about this one, at first glance u might think its impossible to get the square of a number by adding one, however, that number exists, but to fully answer this puzzle you must state where this number 'comes' from not just fill in numbers randomly and get lucky ;)

[gen2]

The answer is the Golden Ratio and is approximately = 1.618 (also -0.618)

It is derived from your statement as follows:

1 + X = X^2
==> X^2 -X -1 =0

to solve a quadratic in X you use the formula:-

X= (-b +or- sqrt(b^2-4ac))/2a

so X = (1 +or- sqrt5)/2

which solves to give you either -0.616 or + 1.618 (to 3 decimal places)

[kempie]

Adding nothing of any consequence to the excellent answer given by gen2, I'm a bit bored at the moment so I thought I would "pretty up" the last equation:

x = � (1 � √5)


Ta da!