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若1/a-1a1=1,求1/a+1a1=
人气:421 ℃ 时间:2021-03-04 04:09:40
解答
1=1/a-|a|,
00.|a|=a,
1=1/a-a,
a=1-a^2,
0=a^2+a-1,Delta=1+4=5
a=[5^(1/2)-1]/2,或a=[-5^(1/2)-1]/2 < 0(舍去)
a=[5^(1/2)-1]/2,
1/a=2/[5^(1/2)-1]=2[5^(1/2)+1]/(5-1)=[5^(1/2)+1]/2,
|a|=[5^(1/2)-1]/2,
1/a+|a|=[5^(1/2)+1]/2 + [5^(1/2)-1]/2 = 5^(1/2)
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