已知x²+x-1=0,试求2008x³+4016x²的值?
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已知x²+x-1=0,试求2008x³+4016x²的值?
已知x²+x-1=0,试求2008x³+4016x²的值?
已知x²+x-1=0,试求2008x³+4016x²的值?
x²+x-1=0
x²=1-x 1-x²=x
x²+x-1=0
x²+2×1/2x+(1/2)²=5/4
(x+1/2)²=(√5/2)²
x+1/2=±√5/2
x=﹣1/2±√5/2
2008x³+4016x²
=2008x³+2×2008x²
=2008x²(x+1)
=2008(1-x)(1+x)
=2008(1-x²)
=2008x
所以2008x³+4016x²
=2008x
=2008×(﹣1/2-√5/2)
=﹣2008×1/2-2008×√5/2
=﹣1004-1004√5
或者
2008x³+4016x²
=2008x
=2008×(﹣1/2+√5/2)
=﹣1004+1004√5
x²+x-1=0
x²+x=1
x²=1-x
所以
2008x³+4016x²
=2008x(1-x)+4016x²
=2008x-2008x²+4016x²
=2008x+2008x²
=2008×(x²+1)
=2008