设a=(√5-1)/2,求(a^5+a^4-2a^3-a^2-a+2)/a^3-a∵2a=√5-12a+1=√54a^2+4a+1=54a^2+4a-4+0a^2+a-1=0∴原式分子=a^3(a^2+a-1)-a^3-a^2-a+2=a^3(a^2+a-1)-a(a^2+a-1)-2a+2∴原式=-2(a-1)/a^3-a=-2(a-1)/a^2(a-1)=-2/a^2解法到这里应该没有问题
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![设a=(√5-1)/2,求(a^5+a^4-2a^3-a^2-a+2)/a^3-a∵2a=√5-12a+1=√54a^2+4a+1=54a^2+4a-4+0a^2+a-1=0∴原式分子=a^3(a^2+a-1)-a^3-a^2-a+2=a^3(a^2+a-1)-a(a^2+a-1)-2a+2∴原式=-2(a-1)/a^3-a=-2(a-1)/a^2(a-1)=-2/a^2解法到这里应该没有问题](/uploads/image/z/3851222-14-2.jpg?t=%E8%AE%BEa%3D%28%E2%88%9A5-1%29%2F2%2C%E6%B1%82%28a%5E5%2Ba%5E4-2a%5E3-a%5E2-a%2B2%29%2Fa%5E3-a%E2%88%B52a%3D%E2%88%9A5-12a%2B1%3D%E2%88%9A54a%5E2%2B4a%2B1%3D54a%5E2%2B4a-4%2B0a%5E2%2Ba-1%3D0%E2%88%B4%E5%8E%9F%E5%BC%8F%E5%88%86%E5%AD%90%3Da%5E3%28a%5E2%2Ba-1%29-a%5E3-a%5E2-a%2B2%3Da%5E3%28a%5E2%2Ba-1%29-a%28a%5E2%2Ba-1%29-2a%2B2%E2%88%B4%E5%8E%9F%E5%BC%8F%3D-2%28a-1%29%2Fa%5E3-a%3D-2%28a-1%29%2Fa%5E2%28a-1%29%3D-2%2Fa%5E2%E8%A7%A3%E6%B3%95%E5%88%B0%E8%BF%99%E9%87%8C%E5%BA%94%E8%AF%A5%E6%B2%A1%E6%9C%89%E9%97%AE%E9%A2%98)
设a=(√5-1)/2,求(a^5+a^4-2a^3-a^2-a+2)/a^3-a∵2a=√5-12a+1=√54a^2+4a+1=54a^2+4a-4+0a^2+a-1=0∴原式分子=a^3(a^2+a-1)-a^3-a^2-a+2=a^3(a^2+a-1)-a(a^2+a-1)-2a+2∴原式=-2(a-1)/a^3-a=-2(a-1)/a^2(a-1)=-2/a^2解法到这里应该没有问题
设a=(√5-1)/2,求(a^5+a^4-2a^3-a^2-a+2)/a^3-a
∵2a=√5-1
2a+1=√5
4a^2+4a+1=5
4a^2+4a-4+0
a^2+a-1=0
∴原式分子=a^3(a^2+a-1)-a^3-a^2-a+2
=a^3(a^2+a-1)-a(a^2+a-1)-2a+2
∴原式=-2(a-1)/a^3-a
=-2(a-1)/a^2(a-1)
=-2/a^2
解法到这里应该没有问题吧,然后呢?
答案是-2,答案用了另一种方法,直接带后不用算什么,这种方法应该也没有错吧,求继续解,要是简单的方法
设a=(√5-1)/2,求(a^5+a^4-2a^3-a^2-a+2)/a^3-a∵2a=√5-12a+1=√54a^2+4a+1=54a^2+4a-4+0a^2+a-1=0∴原式分子=a^3(a^2+a-1)-a^3-a^2-a+2=a^3(a^2+a-1)-a(a^2+a-1)-2a+2∴原式=-2(a-1)/a^3-a=-2(a-1)/a^2(a-1)=-2/a^2解法到这里应该没有问题
原式=-2(a-1)/a^3-a=-2(a-1)/a(a-1)(a+1)
=-2/a^2+a
=-2/1
=-2
你“原式=”后面有一步算错了