a+a分之一等于四求分式(a^4-2a平方1)分之a^4的值
a + 1/a = 4,a^2 - 2a + 1 = 2a,( a - 1 )^2 = 2a;①
a^2 + 2a + 1 = 6a,( a + 1 )^2 = 6a;②
a^2 - 4a + 1 = 0,a = 2 ± √3,a^2 = 7 ± 4√3;③
故 a^4/( a^4 - 2a^2 + 1 )
= a^4/[ a^2 - 1 ]^2
= a^4/[ ( a - 1 )^2 * ( a + 1 )^2 ] 带入 ①、②
= a^4/[ 2a * 6a ]
= a^2/12 带入③
= ( 7 ± 4√3 )/12 。
a+1/a=4,a²=4a-1。
a²+2+1/a²=16,a²-2+1/a²=12。
a^4/(a^4-2a²+1)
=a²/(a²-2+1/a²)
=a²/12
=(4a-1)/12
=a/3-1/12
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