a是一元二次方程x²-2x-2=0的正实数根,则a²-1/a²+a除以(a- (2a-1)/a)
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![a是一元二次方程x²-2x-2=0的正实数根,则a²-1/a²+a除以(a- (2a-1)/a)](/uploads/image/z/578067-51-7.jpg?t=a%E6%98%AF%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8Bx%26%23178%3B-2x-2%3D0%E7%9A%84%E6%AD%A3%E5%AE%9E%E6%95%B0%E6%A0%B9%2C%E5%88%99a%26%23178%3B-1%2Fa%26%23178%3B%2Ba%E9%99%A4%E4%BB%A5%EF%BC%88a-+%282a-1%29%2Fa%EF%BC%89)
a是一元二次方程x²-2x-2=0的正实数根,则a²-1/a²+a除以(a- (2a-1)/a)
a是一元二次方程x²-2x-2=0的正实数根,则a²-1/a²+a除以(a- (2a-1)/a)
a是一元二次方程x²-2x-2=0的正实数根,则a²-1/a²+a除以(a- (2a-1)/a)
∵a是一元二次方程x²-2x-2=0的正实数根
∴a²-2a-2=0
∴(a-1)²=3,∴a=1+√3
∴(a²-1)/(a²+a)÷[a- (2a-1)/a]
=[(a+1)(a-1)/a(a+1)]÷[(a²-2a+1)/a]
=[(a-1)/a]÷[(a-1)²/a]
=[(a-1)/a]×[a/(a-1)²]
=1/(a-1)
=1/(1+√3-1)
=√3/3