Math question

submitted by SkankyDick from self.whatever

X-1=1/X

What is X?

Note: it only needs to be accurate to six digits past the decimal.

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[–]GuyWhite 4 insightful - 1 fun4 insightful - 0 fun5 insightful - 1 fun -  (0 children)

Multiply both sides at the equation by X to get

X2 -X=1

Then subtract 1 from each side to get

X2 -X-1= 0

That’s a quadratic equation of the form aX2 +bX +c = 0

Where, in our case: a=1, b=-1, and c=-1

The formula to solve the quadratic

https://wikimedia.org/api/rest_v1/media/math/render/svg/00c22777378f9c594c71158fea8946f2495f2a28

The calculation works out as shown in u/Panzerdivision ‘s reply

Since quadratic equations have two solutions, OP can pick either solution if just one is wanted.

[–][deleted] 2 insightful - 1 fun2 insightful - 0 fun3 insightful - 1 fun -  (1 child)

2 results:

((√5+1)/2) = 1.61803398875

((-√5+1)/2)= -0.61803398875

[–]SkankyDick[S] 1 insightful - 1 fun1 insightful - 0 fun2 insightful - 1 fun -  (0 children)

Well you are good.

Can you give that to me as a single number?

Edit: I suppose that's close enough.

The golden ratio, also known as the golden number, golden proportion, or divine proportion, is a ratio between two numbers that equals approximately 1.618. It is strongly associated with the Fibonacci sequence, a series of numbers wherein each number is added to the last.0 The origin of this number can be traced back to Euclid, who mentioned it as the "extreme and mean ratio" in the Elements.1 It appears many times in geometry, art, architecture, and other areas.2 In present-day algebra, letting the length of the shorter segment be one unit and the length of the longer segment be x units gives rise to the equation (x + 1)/x = x/1, for which the positive solution is x = (1 + Square root of 5)/2, the golden ratio.

[–]StillLessons 1 insightful - 1 fun1 insightful - 0 fun2 insightful - 1 fun -  (1 child)

1.618034

Why?

[–]SkankyDick[S] 1 insightful - 1 fun1 insightful - 0 fun2 insightful - 1 fun -  (0 children)

I just thought someone might give me a different answer that I wasn't expecting.

I have been tinkering around with the golden ratio off and on for 20 years