已知 X / (X2+X+1) =a,求 X2/(X4+X2+1)=? .说明:X2为X平方,X4为X四次方.非常感谢
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已知 X / (X2+X+1) =a,求 X2/(X4+X2+1)=? .说明:X2为X平方,X4为X四次方.非常感谢
已知 X / (X2+X+1) =a,求 X2/(X4+X2+1)=? .说明:X2为X平方,X4为X四次方.非常感谢
已知 X / (X2+X+1) =a,求 X2/(X4+X2+1)=? .说明:X2为X平方,X4为X四次方.非常感谢
X / (X^2+X+1) =a
1/(x+1+1/x)=a
x+1/x=1/a-1
x^2+1/x^2+2=(1-a)^2/a^2
x^2+1/x^2+1=(1-a)^2/a^2-1=(1-2a)/a^2
X^2/(X^4+X^2+1)= 1 / (x^2+1/x^2+1) = a^2/(1-2a)
X / (X2+X+1) =a
则1/a =(x2+x+1) / x = x +1/x +1
x + 1/x = 1/a -1 两边平方
x2+ 1/x2 +2 = 1/a2 +1- 2/a
x2+1/x2 =1/a2 -2/a -1
(x4+x2+1)/ x2 =x2 +1/x2 +1 =1/a2 -2/a =(1-2a)/a2
X2/(X4+X2+1)= a2/(1-2a)
答案:a^/(1-2a)
这道题很简单啦其实。
姐姐提醒你一下哦,只需把已知条件变成倒数,待求问题也变成倒数,相信小家伙就能看出玄机啦
X / (X2+X+1) =a
左边同除X
x+1/x=1/a-1
两边平方
x2+1/x2=1/a2-2/a-1
X2/(X4+X2+1)
=1/(x2+1/x2+1)
=a2/(2a2-2a+1)
a=X / (X^2+X+1) =1/(x+1/x+1)
∴x+1+1/x=1/a
∴x+1/x=1/a-1
∴(x+1/x)^2=(1/a-1)^2=1/a^2-2/a+1
即:x^2+2+1/x^2=1/a^2-2/a+1
∴x^2+1+1/x^2=1/a^2-2/a=(1-2a)/a^2
∴1/(x^2+1+1/x^2)=a^2/(1-2a)
∴X^2/(X^4+X2+1)=1/(x^2+1+1/x^2)=a^2/(1-2a)