若a是方程x² x-1=0的根,求代数式2000a³ 4000a²的值x²+x-1,2000a³+4000a²
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![若a是方程x² x-1=0的根,求代数式2000a³ 4000a²的值x²+x-1,2000a³+4000a²](/uploads/image/z/647868-12-8.jpg?t=%E8%8B%A5a%E6%98%AF%E6%96%B9%E7%A8%8Bx%26%23178%3B+x-1%3D0%E7%9A%84%E6%A0%B9%2C%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F2000a%26%23179%3B+4000a%26%23178%3B%E7%9A%84%E5%80%BCx%26%23178%3B%2Bx-1%2C2000a%26%23179%3B%2B4000a%26%23178%3B)
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若a是方程x² x-1=0的根,求代数式2000a³ 4000a²的值x²+x-1,2000a³+4000a²
若a是方程x² x-1=0的根,求代数式2000a³ 4000a²的值
x²+x-1,2000a³+4000a²
若a是方程x² x-1=0的根,求代数式2000a³ 4000a²的值x²+x-1,2000a³+4000a²
∵a是方程x² +x-1=0的根
∴a²+a-1=0
∴2000a³ +4000a²
=2000a³+2000a²-2000a+2000a²+2000a-2000+2000
=2000a(a²+a-1)+2000(a²+a-1)+2000
∵a²+a-1=0
∴原式=2000a×0 +2000×0+2000
=2000
a是方程x² +x-1=0的根
∴a²+a=1
2000a³+4000a²
=2000a(a²+a)+2000a²
=2000a+2000a²
=2000(a²+a)
=2000