Does anyone recognize this real number?

[Stush]

2.41421356237... or its reciprocal 0.414213562373

(Last digit might have been rounded.)

Thanks!

[Dennis May]

Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!

Looks like sqrt(2)+1 and its reciprocal sqrt(2)-1.

[Zdislav V. Kovarik]

Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!

Call the first number x, then the second number is 1/x,
as you said, and look at x - 1/x. Which positive x will fit the arising
equation?

(Others, I am sure, will do the algebra for you. Oh well..)

Cheers, ZVK(Slavek).

[JEMebius]

x - 1/x = 2 --> x^2 - 2x - 1 = 0 --> x = 1 + sqrt(2) or x = 1 -
sqrt(2); x = 1 + sqrt(2) fits your question.

Please read in any high school algebra textbook how to solve quatratic
equations.

HTH: Johan E. Mebius

==============

Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!

[Oscar Lanzi III]

The number minus its reciprocal is 2. Thus 1/x = x-2. Clear fractions
and solve for the positive root of the resulting quadratic equation.

--OL

[Richard Henry]

Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!

2+n = 1/n?

I always liked 1+n = 1/n, which is very close to the ratio between miles and
kilometers.

[Stush]

Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!

sqrt(2) + 1 = 2.41421356237...

lim n->infinity P(n+1)/P(n) = sqrt(2) + 1
where P(n) is the nth Pell number.

Though I assume this result is well known.