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a,b,c成GP
b^2=ac b=(ac)^(1/2)
a,x,b和b,y,c成AP
2*x=a+b x=(a+b)/2
2*y=b+c y=(b+c)/2
a/x+c/y
=a/[ (a+b)/2 ] +c/[ (b+c)/2 ]
=2{ a/[a+(ac)^(1/2)] + c/[ c+(ac)^(1/2)]
a=[(a)^(1/2)]^2
c=[(c)^(1/2)]^2
a/x+c/y
=2*{[a^(1/2)]/[a^(1/2) +c^(1/2)]+[c^(1/2)]/[a^(1/2) +c^(1/2)]}
=2*{[a^(1/2) +c^(1/2)]/[a^(1/2) +c^(1/2)]}
=2
b^2=ac b=(ac)^(1/2)
a,x,b和b,y,c成AP
2*x=a+b x=(a+b)/2
2*y=b+c y=(b+c)/2
a/x+c/y
=a/[ (a+b)/2 ] +c/[ (b+c)/2 ]
=2{ a/[a+(ac)^(1/2)] + c/[ c+(ac)^(1/2)]
a=[(a)^(1/2)]^2
c=[(c)^(1/2)]^2
a/x+c/y
=2*{[a^(1/2)]/[a^(1/2) +c^(1/2)]+[c^(1/2)]/[a^(1/2) +c^(1/2)]}
=2*{[a^(1/2) +c^(1/2)]/[a^(1/2) +c^(1/2)]}
=2
1年前
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