a^2-1分之a-2除以(a-1-a+1分之2a-1),其中a是方程x^2-x=根号3的根

问题描述:

a^2-1分之a-2除以(a-1-a+1分之2a-1),其中a是方程x^2-x=根号3的根

=√3/3

化简以后等于1/(a^2-a)
又因为a是X^2-X=√3的解
则a^2-a=√3
所以1/(a^2-a)=1/√3=√3/3

(a-2)/(a²-1) ÷ (a-1)-(2a-1/a+1)=(a-2)/(a²-1) ÷ [(a+1)(a-1)-(2a-1)]/a+1)=(a-2)/(a²-1) ÷ (a²-2a/a+1)=[(a-2)/(a+1)(a-1)]x(a+1)/a(a-2)=1/(a²-a)a是方...

∵a是方程x^2-x=根号3的根
∴a²-a=√3
∴(a-2)/(a^2-1) ÷[a-1-(2a-1)/(a+1)]
=(a-2)/(a^2-1) ÷[(a²-1)/(a+1)-(2a-1)/(a+1)]
=(a-2)/(a^2-1) ÷[(a²-2a)/(a+1)]
=(a-2)/[(a-1)(a+1)]*(a+1)/[a(a-2)]
=1/[a(a-1)]
=1/(a²-a)
=1/√3
=√3/3

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