質問: 2=[(a+b)/a]^2如何得知a:b=(√2+1):1? 2=[(a+b)/a]^2如何得知a:b=(√2+1):1?
回答: 2 = [(a+b)/a]^2 = (1+b/a)^2 ∴ 1 + b/a = ±√2 若 a>0 且 b>0, 則 1+b/a = √2 ∴ b/a = √2 - 1 即 b:a = √2-1:1 或即 a:b = 1 : √2-1 = √2+1 : 1