Wolfram's knowledge base is wrong when it comes to what the Golden Ratio Conjugate is, as of 2/25/25. Wolfram states that the value is roughly .618033988749894, when in all actuality the value is the negative of that value.
That is, the value is approximately -0.618033988749894
The formula for the GR and the GRC is as follows:
x² - x - 1 = 0
which solves as...
(1 ± √5) / 2
which solves as (approximately)...
1.61803398875 (Golden Ratio)
and
-0.61803398874 (Golden Ratio Conjugate)
Enjoy!