what is one number whose reciprocal is one less than itself?
- DouglasLv 77 years agoFavorite Answer
x = 1/x + 1
x² = 1 + x
x² – x – 1 = 0 quadratic formula
x = 1.618 or x = – 0.61803
- poornakumar bLv 77 years ago
" ? " has beaten me by 18 minutes. He gave the exact answer. The (irrational) number is called 'Phi',
φ = ½ [√5±1].
Further the square of the number is 'one more than itself'. That is
φ² = φ + 1 = 2.6180.
The equation stems from what ' ? ' derived.
In Trigonometry, functions of multiples of 18º (= π/10) are expressed as functions involving φ,
Sin [n(π/10)], Cos [n(π/10)] = f(φ).
It has several more Mathematical uses & is a hot favourite of 'Architects' who call it 'Magic number'. A rectangle of these proportions is the most aesthetic in architecture (le Corbusier used it extensively in proportioning his buildings in his town planning of a new city - Chandigarh).
- 7 years ago