若b/a=1+√2,则2ab/(a^2+b^2)=?

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若b/a=1+√2,则2ab/(a^2+b^2)=?

若b/a=1+√2,则2ab/(a^2+b^2)=?
若b/a=1+√2,则2ab/(a^2+b^2)=?

若b/a=1+√2,则2ab/(a^2+b^2)=?
∴b/a=1+√2 ∴ a/b=1/(1+√2)=√2-1
2ab/(a²+b²) 式子的分子分母分别除以ab得 原式=2/(b/a+a/b)=2/(1+√2+√2-1)=√2/2

1+√2/2+√2

=(2b/a)/(1+(b/a)^2)
=(2+2根号2)/(1+(1+根号2)^2)
=(2+2根号2)/(4+2根号2)
=(1+根号2)/(2+根号2)
=根号2/2

b/a=1+√2
平方
b^2/a^2=3+2√2
2ab/(a^2+b^2)
上下同除以a^2
=2(b/a)[1+(b/a)^2]
=2(1+√2)/(1+3+2√2)
=2(√2+1)/[2(2+√2)]
=(√2+1)(2-√2)/(2+√2)(2-√2)
=(2√2-2+2-√2)/(4-2)
=√2/2