Respuesta :
Golden Ratio?
a/b=b/(a+b)
a^2+ab=b^2
b^2-ab-a^2=0
b=(a(+-)(a^2+4a^2)^(1/2))/2
b=(a+a(5)^(1/2))/2
b≈1.618
a/b=b/(a+b)
a^2+ab=b^2
b^2-ab-a^2=0
b=(a(+-)(a^2+4a^2)^(1/2))/2
b=(a+a(5)^(1/2))/2
b≈1.618
Answer:
Step-by-step explanation:
Golden ratio is a special number found by dividing a line into two parts so that longer part is divided by the smaller one is equal to whole length divided by longer one.
a/b = (a + b)/a
a² = b(a + b)
a² = ab + b²
a² - ab - b² = 0
Now from the quadratic equation
a = [+b ± √(b² + 4b²)]/2
a = b×[1 ± √(5]/2
a/b = (1 + 2.236)/2 = 3.236/2 = 1.6180
This is the golden ratio is 1.6180 denoted by Phi.
